Journal articles: 'Forcing theory'

1

Zapletal, Jindřich. "Dimension theory and forcing." Topology and its Applications 167 (April 2014): 31–35. http://dx.doi.org/10.1016/j.topol.2014.03.004.

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2

Avigad, Jeremy. "Forcing in Proof Theory." Bulletin of Symbolic Logic 10, no. 3 (September 2004): 305–33. http://dx.doi.org/10.2178/bsl/1102022660.

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AbstractPaul Cohen's method of forcing, together with Saul Kripke's related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mathematical logic, from set theory and model theory to constructive and categorical logic. Here, I argue that forcing also has a place in traditional Hilbert-style proof theory, where the goal is to formalize portions of ordinary mathematics in restricted axiomatic theories, and study those theories in constructive or syntactic terms. I will discuss the aspects of forcing that are useful in this respect, and some sample applications. The latter include ways of obtaining conservation results for classical and intuitionistic theories, interpreting classical theories in constructive ones, and constructivizing model-theoretic arguments.

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3

Komjath, Peter. "Ramsey-Theory and Forcing Extensions." Proceedings of the American Mathematical Society 121, no. 1 (May 1994): 217. http://dx.doi.org/10.2307/2160385.

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Komjáth, Péter. "Ramsey theory and forcing extensions." Proceedings of the American Mathematical Society 121, no. 1 (January 1, 1994): 217. http://dx.doi.org/10.1090/s0002-9939-1994-1169039-2.

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5

Baldwin, J. T., M. C. Laskowski, and S. Shelah. "Forcing isomorphism." Journal of Symbolic Logic 58, no. 4 (December 1993): 1291–301. http://dx.doi.org/10.2307/2275144.

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If two models of a first-order theory are isomorphic, then they remain isomorphic in any forcing extension of the universe of sets. In general however, such a forcing extension may create new isomorphisms. For example, any forcing that collapses cardinals may easily make formerly nonisomorphic models isomorphic. However, if we place restrictions on the partially-ordered set to ensure that the forcing extension preserves certain invariants, then the ability to force nonisomorphic models of some theory T to be isomorphic implies that the invariants are not sufficient to characterize the models of T.A countable first-order theory is said to be classifiable if it is superstable and does not have either the dimensional order property (DOP) or the omitting types order property (OTOP). If T is not classifiable, Shelah has shown in [5] that sentences in L∞,λ do not characterize models of T of power λ. By contrast, in [8] Shelah showed that if a theory T is classifiable, then each model of cardinality λ is described by a sentence of L∞,λ. In fact, this sentence can be chosen in the . ( is the result of enriching the language by adding for each μ < λ a quantifier saying the dimension of a dependence structure is greater than μ) Further work ([3], [2]) shows that ⊐+ can be replaced by ℵ1.

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6

Zapletal, Jindřich. "Descriptive set theory and definable forcing." Memoirs of the American Mathematical Society 167, no. 793 (2004): 0. http://dx.doi.org/10.1090/memo/0793.

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7

Spinas, O. "Iterated forcing in quadratic form theory." Israel Journal of Mathematics 79, no. 2-3 (October 1992): 297–315. http://dx.doi.org/10.1007/bf02808222.

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8

Krueger, John, and Miguel Angel Mota. "Coherent adequate forcing and preserving CH." Journal of Mathematical Logic 15, no. 02 (December 2015): 1550005. http://dx.doi.org/10.1142/s0219061315500051.

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We develop a general framework for forcing with coherent adequate sets on [Formula: see text] as side conditions, where [Formula: see text] is a cardinal of uncountable cofinality. We describe a class of forcing posets which we call coherent adequate type forcings. The main theorem of the paper is that any coherent adequate type forcing preserves CH. We show that there exists a forcing poset for adding a club subset of [Formula: see text] with finite conditions while preserving CH, solving a problem of Friedman [Forcing with finite conditions, in Set Theory: Centre de Recerca Matemática, Barcelona, 2003–2004, Trends in Mathematics (Birkhäuser-Verlag, 2006), pp. 285–295.].

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9

Viale, Matteo. "Category forcings, ${MM}^{+++}$, and generic absoluteness for the theory of strong forcing axioms." Journal of the American Mathematical Society 29, no. 3 (August 19, 2015): 675–728. http://dx.doi.org/10.1090/jams/844.

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10

Henderson, G. H., and S. Fleeter. "Forcing Function Effects on Unsteady Aerodynamic Gust Response: Part 1—Forcing Functions." Journal of Turbomachinery 115, no. 4 (October 1, 1993): 741–50. http://dx.doi.org/10.1115/1.2929309.

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The fundamental gust modeling assumption is investigated by means of a series of experiments performed in the Purdue Annular Cascade Research Facility. The unsteady periodic flow field is generated by rotating rows of perforated plates and airfoil cascades. In this paper, the measured unsteady flow fields are compared to linear-theory vortical gust requirements, with the resulting unsteady gust response of a downstream stator cascade correlated with linear theory predictions in an accompanying paper. The perforated-plate forcing functions closely resemble linear-theory forcing functions, with the static pressure fluctuations small and the periodic velocity vectors parallel to the downstream mean-relative flow angle over the entire periodic cycle. In contrast, the airfoil forcing functions exhibit characteristics far from linear-theory vortical gusts, with the alignment of the velocity vectors and the static pressure fluctuation amplitudes dependent on the rotor-loading condition, rotor solidity, and the inlet mean-relative flow angle. Thus, these unique data clearly show that airfoil wakes, both compressor and turbine, are not able to be modeled with the boundary conditions of current state-of-the-art linear unsteady aerodynamic theory.

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11

ZAPLETAL, JINDŘICH. "SEPARATION PROBLEMS AND FORCING." Journal of Mathematical Logic 13, no. 01 (May 28, 2013): 1350002. http://dx.doi.org/10.1142/s0219061313500025.

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Certain separation problems in descriptive set theory correspond to a forcing preservation property, with a fusion type infinite game associated to it. As an application, it is consistent with the axioms of set theory that the circle 𝕋 can be covered by ℵ1 many closed sets of uniqueness while a much larger number of H-sets is necessary to cover it.

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12

Poveda, Alejandro. "Contributions to the Theory of Large Cardinals through the Method of Forcing." Bulletin of Symbolic Logic 27, no. 2 (June 2021): 221–22. http://dx.doi.org/10.1017/bsl.2021.22.

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AbstractThe dissertation under comment is a contribution to the area of Set Theory concerned with the interactions between the method of Forcing and the so-called Large Cardinal axioms.The dissertation is divided into two thematic blocks. In Block I we analyze the large-cardinal hierarchy between the first supercompact cardinal and Vopěnka’s Principle (Part I). In turn, Block II is devoted to the investigation of some problems arising from Singular Cardinal Combinatorics (Part II and Part III).We commence Part I by investigating the Identity Crisis phenomenon in the region comprised between the first supercompact cardinal and Vopěnka’s Principle. As a result, we generalize Magidor’s classical theorems [2] to this higher region of the large-cardinal hierarchy. Also, our analysis allows to settle all the questions that were left open in [1]. Finally, we conclude Part I by presenting a general theory of preservation of $C^{(n)}$ -extendible cardinals under class forcing iterations. From this analysis we derive several applications. For instance, our arguments are used to show that an extendible cardinal is consistent with “ $(\lambda ^{+\omega })^{\mathrm {HOD}}<\lambda ^+$ , for every regular cardinal $\lambda $ .” In particular, if Woodin’s HOD Conjecture holds, and therefore it is provable in ZFC + “There exists an extendible cardinal” that above the first extendible cardinal every singular cardinal $\lambda $ is singular in HOD and $(\lambda ^+)^{\textrm {{HOD}}}=\lambda ^+$ , there may still be no agreement at all between V and HOD about successors of regular cardinals.In Part II and Part III we analyse the relationship between the Singular Cardinal Hypothesis (SCH) with other relevant combinatorial principles at the level of successors of singular cardinals. Two of these are the Tree Property and the Reflection of Stationary sets, which are central in Infinite Combinatorics.Specifically, Part II is devoted to prove the consistency of the Tree Property at both $\kappa ^+$ and $\kappa ^{++}$ , whenever $\kappa $ is a strong limit singular cardinal witnessing an arbitrary failure of the SCH. This generalizes the main result of [3] in two senses: it allows arbitrary cofinalities for $\kappa $ and arbitrary failures for the SCH.In the last part of the dissertation (Part III) we introduce the notion of $\Sigma $ -Prikry forcing. This new concept allows an abstract and uniform approach to the theory of Prikry-type forcings and encompasses several classical examples of Prikry-type forcing notions, such as the classical Prikry forcing, the Gitik-Sharon poset, or the Extender Based Prikry forcing, among many others.Our motivation in this part of the dissertation is to prove an iteration theorem at the level of the successor of a singular cardinal. Specifically, we aim for a theorem asserting that every $\kappa ^{++}$ -length iteration with support of size $\leq \kappa $ has the $\kappa ^{++}$ -cc, provided the iterates belong to a relevant class of $\kappa ^{++}$ -cc forcings. While there are a myriad of works on this vein for regular cardinals, this contrasts with the dearth of investigations in the parallel context of singular cardinals. Our main contribution is the proof that such a result is available whenever the class of forcings under consideration is the family of $\Sigma $ -Prikry forcings. Finally, and as an application, we prove that it is consistent—modulo large cardinals—the existence of a strong limit cardinal $\kappa $ with countable cofinality such that $\mathrm {SCH}_\kappa $ fails and every finite family of stationary subsets of $\kappa ^+$ reflects simultaneously.

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13

ANTOS, CAROLIN, and SY-DAVID FRIEDMAN. "HYPERCLASS FORCING IN MORSE-KELLEY CLASS THEORY." Journal of Symbolic Logic 82, no. 2 (June 2017): 549–75. http://dx.doi.org/10.1017/jsl.2016.74.

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AbstractIn this article we introduce and study hyperclass-forcing (where the conditions of the forcing notion are themselves classes) in the context of an extension of Morse-Kelley class theory, called MK**. We define this forcing by using a symmetry between MK** models and models of ZFC− plus there exists a strongly inaccessible cardinal (called SetMK**). We develop a coding between β-models ${\cal M}$ of MK** and transitive models M+ of SetMK** which will allow us to go from ${\cal M}$ to M+ and vice versa. So instead of forcing with a hyperclass in MK** we can force over the corresponding SetMK** model with a class of conditions. For class-forcing to work in the context of ZFC− we show that the SetMK** model M+ can be forced to look like LK*[X], where κ* is the height of M+, κ strongly inaccessible in M+ and $X \subseteq \kappa$. Over such a model we can apply definable class forcing and we arrive at an extension of M+ from which we can go back to the corresponding β-model of MK**, which will in turn be an extension of the original ${\cal M}$. Our main result combines hyperclass forcing with coding methods of [3] and [4] to show that every β-model of MK** can be extended to a minimal such model of MK** with the same ordinals. A simpler version of the proof also provides a new and analogous minimality result for models of second-order arithmetic.

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14

Coquand, Thierry, and Guilhem Jaber. "A Note on Forcing and Type Theory." Fundamenta Informaticae 100, no. 1-4 (2010): 43–52. http://dx.doi.org/10.3233/fi-2010-262.

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15

Slaman, Theodore A. "Reflection and forcing in E-recursion theory." Annals of Pure and Applied Logic 29, no. 1 (July 1985): 79–106. http://dx.doi.org/10.1016/0168-0072(85)90036-3.

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16

Zhang, Lei, and Rafael de la Llave. "Transition state theory with quasi-periodic forcing." Communications in Nonlinear Science and Numerical Simulation 62 (September 2018): 229–43. http://dx.doi.org/10.1016/j.cnsns.2018.02.014.

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17

Maxson, C. J., and J. H. Meyer. "Forcing Linearity Numbers." Journal of Algebra 223, no. 1 (January 2000): 190–207. http://dx.doi.org/10.1006/jabr.1999.7991.

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18

Golmohamadian, M., M. M. Zahedi, and N. Soltankhah. "Some algebraic hyperstructures related to zero forcing sets and forcing digraphs." Journal of Algebra and Its Applications 18, no. 10 (August 6, 2019): 1950192. http://dx.doi.org/10.1142/s0219498819501925.

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A zero forcing set is a new concept in Graph Theory which was introduced in recent years. In this paper, we investigate the relationship between zero forcing sets and algebraic hyperstructures. To this end, we present some new definitions by considering a zero forcing process on a graph [Formula: see text]. These definitions help us analyze the zero forcing process better and construct various hypergroups and join spaces on the vertex set of graph [Formula: see text]. Finally, we give some examples to clarify these hyperstructures.

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19

Liu, Zhengyu, Yishuai Jin, and Xinyao Rong. "A Theory for the Seasonal Predictability Barrier: Threshold, Timing, and Intensity." Journal of Climate 32, no. 2 (December 21, 2018): 423–43. http://dx.doi.org/10.1175/jcli-d-18-0383.1.

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Abstract A theory is developed in a stochastic climate model for understanding the general features of the seasonal predictability barrier (PB), which is characterized by a band of maximum decline in autocorrelation function phase-locked to a particular season. Our theory determines the forcing threshold, timing, and intensity of the seasonal PB as a function of the damping rate and seasonal forcing. A seasonal PB is found to be an intrinsic feature of a stochastic climate system forced by either seasonal growth rate or seasonal noise forcing. A PB is generated when the seasonal forcing, relative to the damping rate, exceeds a modest threshold. Once generated, all the PBs occur in the same calendar month, forming a seasonal PB. The PB season is determined by the decline of the seasonal forcing as well as the delayed response associated with damping. As such, for a realistic weak damping, the PB season is locked close to the minimum SST variance under the seasonal growth-rate forcing, but after the minimum SST variance under the seasonal noise forcing. The intensity of the PB is determined mainly by the amplitude of the seasonal forcing. The theory is able to explain the general features of the seasonal PB of the observed SST variability over the world. In the tropics, a seasonal PB is generated mainly by a strong seasonal growth rate, whereas in the extratropics a seasonal PB is generated mainly by a strong seasonal noise forcing. Our theory provides a general framework for the understanding of the seasonal PB of climate variability.

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20

Kanamori, Akihiro. "Cohen and Set Theory." Bulletin of Symbolic Logic 14, no. 3 (September 2008): 351–78. http://dx.doi.org/10.2178/bsl/1231081371.

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21

Judah, Haim, Andrzej Rosłanowski, and Saharon Shelah. "Examples for Souslin forcing." Fundamenta Mathematicae 144, no. 1 (1994): 23–42. http://dx.doi.org/10.4064/fm-144-1-23-42.

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22

Le Calvez, P., and F. A. Tal. "Forcing theory for transverse trajectories of surface homeomorphisms." Inventiones mathematicae 212, no. 2 (December 8, 2017): 619–729. http://dx.doi.org/10.1007/s00222-017-0773-x.

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23

Audrito, Giorgio, and Matteo Viale. "Absoluteness via resurrection." Journal of Mathematical Logic 17, no. 02 (November 27, 2017): 1750005. http://dx.doi.org/10.1142/s0219061317500052.

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The resurrection axioms are forcing axioms introduced recently by Hamkins and Johnstone, developing on ideas of Chalons and Veličković. We introduce a stronger form of resurrection axioms (the iterated resurrection axioms [Formula: see text] for a class of forcings [Formula: see text] and a given ordinal [Formula: see text]), and show that [Formula: see text] implies generic absoluteness for the first-order theory of [Formula: see text] with respect to forcings in [Formula: see text] preserving the axiom, where [Formula: see text] is a cardinal which depends on [Formula: see text] ([Formula: see text] if [Formula: see text] is any among the classes of countably closed, proper, semiproper, stationary set preserving forcings). We also prove that the consistency strength of these axioms is below that of a Mahlo cardinal for most forcing classes, and below that of a stationary limit of supercompact cardinals for the class of stationary set preserving posets. Moreover, we outline that simultaneous generic absoluteness for [Formula: see text] with respect to [Formula: see text] and for [Formula: see text] with respect to [Formula: see text] with [Formula: see text] is in principle possible, and we present several natural models of the Morse–Kelley set theory where this phenomenon occurs (even for all [Formula: see text] simultaneously). Finally, we compare the iterated resurrection axioms (and the generic absoluteness results we can draw from them) with a variety of other forcing axioms, and also with the generic absoluteness results by Woodin and the second author.

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24

Kunen, Kenneth. "Forcing and Differentiable Functions." Order 29, no. 2 (April 1, 2011): 293–310. http://dx.doi.org/10.1007/s11083-011-9210-8.

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25

BALDWIN, STEWART. "TOWARD A THEORY OF FORCING ON MAPS OF TREES." International Journal of Bifurcation and Chaos 05, no. 05 (October 1995): 1307–18. http://dx.doi.org/10.1142/s0218127495000971.

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The "forcing" relation on patterns of invariant subsets of maps on the interval has proved to be a useful tool for studying the dynamics of interval maps. However, attempts to generalize this relation to more general spaces (such as trees) have met with difficulties. A new relation is introduced, which is well-defined for all continuous maps on any dendrite, is closely related to the forcing relation on the unit interval, and has at least some of the nice properties on trees which one would expect from a generalized forcing relation.

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26

Streicher, Thomas. "Forcing for IZF in Sheaf Toposes." gmj 16, no. 1 (March 2009): 203–9. http://dx.doi.org/10.1515/gmj.2009.203.

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Abstract In [Category-theoretic models for intuitionistic set theory, 1985] D. Scott showed how the interpretation of intuitionistic set theory IZF in presheaf toposes can be reformulated in a more concrete fashion à la forcing as known to set theorists. In this note we show how this can be adapted to the more general case of Grothendieck toposes dealt with abstractly in [Fourman, J. Pure Appl. Algebra 19: 91–101, 1980, Hayashi, On set theories in toposes, Springer, 1981].

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27

Aichinger, Erhard. "Congruence lattices forcing nilpotency." Journal of Algebra and Its Applications 17, no. 02 (January 23, 2018): 1850033. http://dx.doi.org/10.1142/s0219498818500330.

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Given a lattice [Formula: see text] and a class [Formula: see text] of algebraic structures, we say that [Formula: see text] forces nilpotency in [Formula: see text] if every algebra [Formula: see text] whose congruence lattice [Formula: see text] is isomorphic to [Formula: see text] is nilpotent. We describe congruence lattices that force nilpotency, supernilpotency or solvability for some classes of algebras. For this purpose, we investigate which commutator operations can exist on a given congruence lattice.

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28

Bobok, Jozef. "Forcing relation on interval patterns." Fundamenta Mathematicae 187, no. 1 (2005): 37–60. http://dx.doi.org/10.4064/fm187-1-2.

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29

Bagaria, Joan, and Roger Bosch. "Generic absoluteness under projective forcing." Fundamenta Mathematicae 194, no. 2 (2007): 95–120. http://dx.doi.org/10.4064/fm194-2-1.

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30

Wehrung, Friedrich. "Forcing extensions of partial lattices." Journal of Algebra 262, no. 1 (April 2003): 127–93. http://dx.doi.org/10.1016/s0021-8693(03)00015-2.

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31

Klein, Douglas J., and Vladimir Rosenfeld. "Forcing, Freedom, & Uniqueness in Graph Theory & Chemistry." Croatica Chemica Acta 87, no. 1 (2014): 49–59. http://dx.doi.org/10.5562/cca2000.

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32

Kislov, A. V. "Astronomical forcing and mathematical theory of glacial-interglacial cycles." Climate of the Past Discussions 5, no. 1 (February 9, 2009): 327–40. http://dx.doi.org/10.5194/cpd-5-327-2009.

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Abstract. There are three important features of a proxy time series recorded during the Late Pleistocene. They are: 1) 100 000-year cycle as a dominant control of global glacial-interglacials through the late Quaternary, 2) fluctuations with periods of about 40 and 20 thousand years (their contribution to dispersion is no more than 20%), 3) ''Red-noise'' behavior of the time series. Direct influence of the insolation change created by fluctuations of the eccentricity is too weak to cause the observed 100 000-year climate fluctuations. Therefore, other mechanisms of such a rhythm are proposed. On the basis of the equation of the heat budget, the equation describing dynamics of zonally averaged temperature is developed. Various combinations of terms of this equation are discussed. They present a linear response to the Milankovitch periodicity, the Langeven stochastic equation, the equation of delay oscillator, the stochastic equation of spontaneous transitions, and the equation of stochastic resonance. Orbitally-induced changes in the solar energy flux received by the Earth play an important role as a mechanism starting process of climate changes which is supported and intensified by different feedbacks within the climate system. Positive anomalies of solar radiation serve as a mechanism causing reorganization of the climate only in rare cases when inclination of Earth axis of rotation increases and, simultaneously, perihelion takes place during the summer time (for the Northern Hemisphere).

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Rüdiger, Sten, Ernesto M. Nicola, Jaume Casademunt, and Lorenz Kramer. "Theory of pattern forming systems under traveling-wave forcing." Physics Reports 447, no. 3-6 (August 2007): 73–111. http://dx.doi.org/10.1016/j.physrep.2007.02.017.

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Boychuk Duchscher, Judy E., and Debra Morgan. "Grounded theory: reflections on the emergence vs. forcing debate." Journal of Advanced Nursing 48, no. 6 (December 2004): 605–12. http://dx.doi.org/10.1111/j.1365-2648.2004.03249.x.

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35

Neeman, Itay, and Jindřich Zapletal. "Proper forcing and L(ℝ)." Journal of Symbolic Logic 66, no. 2 (June 2001): 801–10. http://dx.doi.org/10.2307/2695045.

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AbstractWe present two ways in which the model L(ℝ) is canonical assuming the existence of large cardinals. We show that the theory of this model, with ordinal parameters, cannot be changed by small forcing: we show further that a set of ordinals in V cannot be added to L(ℝ) by small forcing. The large cardinal needed corresponds to the consistency strength of ADL(ℝ): roughly ω Woodin cardinals.

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Schlindwein, Chaz. "Shelah's work on non-semi-proper iterations, II." Journal of Symbolic Logic 66, no. 4 (December 2001): 1865–83. http://dx.doi.org/10.2307/2694981.

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One of the main goals in the theory of forcing iteration is to formulate preservation theorems for not collapsing ω1 which are as general as possible. This line leads from c.c.c. forcings using finite support iterations to Axiom A forcings and proper forcings using countable support iterations to semi-proper forcings using revised countable support iterations, and more recently, in work of Shelah, to yet more general classes of posets. In this paper we concentrate on a special case of the very general iteration theorem of Shelah from [5, chapter XV]. The class of posets handled by this theorem includes all semi-proper posets and also includes, among others, Namba forcing.In [5, chapter XV] Shelah shows that, roughly, revised countable support forcing iterations in which the constituent posets are either semi-proper or Namba forcing or P[W] (the forcing for collapsing a stationary co-stationary subset ofwith countable conditions) do not collapse ℵ1. The iteration must contain sufficiently many cardinal collapses, for example, Levy collapses. The most easily quotable combinatorial application is the consistency (relative to a Mahlo cardinal) of ZFC + CH fails + whenever A ∪ B = ω2 then one of A or B contains an uncountable sequentially closed subset. The iteration Shelah uses to construct this model is built using P[W] to “attack” potential counterexamples, Levy collapses to ensure that the cardinals collapsed by the various P[W]'s are sufficiently well separated, and Cohen forcings to ensure the failure of CH in the final model.In this paper we give details of the iteration theorem, but we do not address the combinatorial applications such as the one quoted above.These theorems from [5, chapter XV] are closely related to earlier work of Shelah [5, chapter XI], which dealt with iterated Namba and P[W] without allowing arbitrary semi-proper forcings to be included in the iteration. By allowing the inclusion of semi-proper forcings, [5, chapter XV] generalizes the conjunction of [5, Theorem XI.3.6] with [5, Conclusion XI.6.7].

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37

Terborgh, John W. "Toward a trophic theory of species diversity." Proceedings of the National Academy of Sciences 112, no. 37 (September 15, 2015): 11415–22. http://dx.doi.org/10.1073/pnas.1501070112.

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Efforts to understand the ecological regulation of species diversity via bottom-up approaches have failed to yield a consensus theory. Theories based on the alternative of top-down regulation have fared better. Paine’s discovery of keystone predation demonstrated that the regulation of diversity via top-down forcing could be simple, strong, and direct, yet ecologists have persistently failed to perceive generality in Paine’s result. Removing top predators destabilizes many systems and drives transitions to radically distinct alternative states. These transitions typically involve community reorganization and loss of diversity, implying that top-down forcing is crucial to diversity maintenance. Contrary to the expectations of bottom-up theories, many terrestrial herbivores and mesopredators are capable of sustained order-of-magnitude population increases following release from predation, negating the assumption that populations of primary consumers are resource limited and at or near carrying capacity. Predationsensu lato(to include Janzen–Connell mortality agents) has been shown to promote diversity in a wide range of ecosystems, including rocky intertidal shelves, coral reefs, the nearshore ocean, streams, lakes, temperate and tropical forests, and arctic tundra. The compelling variety of these ecosystems suggests that top-down forcing plays a universal role in regulating diversity. This conclusion is further supported by studies showing that the reduction or absence of predation leads to diversity loss and, in the more dramatic cases, to catastrophic regime change. Here, I expand on the thesis that diversity is maintained by the interaction between predation and competition, such that strong top-down forcing reduces competition, allowing coexistence.

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Ramaswamy, V., W. Collins, J. Haywood, J. Lean, N. Mahowald, G. Myhre, V. Naik, et al. "Radiative Forcing of Climate: The Historical Evolution of the Radiative Forcing Concept, the Forcing Agents and their Quantification, and Applications." Meteorological Monographs 59 (January 1, 2019): 14.1–14.101. http://dx.doi.org/10.1175/amsmonographs-d-19-0001.1.

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Abstract We describe the historical evolution of the conceptualization, formulation, quantification, application, and utilization of “radiative forcing” (RF) of Earth’s climate. Basic theories of shortwave and longwave radiation were developed through the nineteenth and twentieth centuries and established the analytical framework for defining and quantifying the perturbations to Earth’s radiative energy balance by natural and anthropogenic influences. The insight that Earth’s climate could be radiatively forced by changes in carbon dioxide, first introduced in the nineteenth century, gained empirical support with sustained observations of the atmospheric concentrations of the gas beginning in 1957. Advances in laboratory and field measurements, theory, instrumentation, computational technology, data, and analysis of well-mixed greenhouse gases and the global climate system through the twentieth century enabled the development and formalism of RF; this allowed RF to be related to changes in global-mean surface temperature with the aid of increasingly sophisticated models. This in turn led to RF becoming firmly established as a principal concept in climate science by 1990. The linkage with surface temperature has proven to be the most important application of the RF concept, enabling a simple metric to evaluate the relative climate impacts of different agents. The late 1970s and 1980s saw accelerated developments in quantification, including the first assessment of the effect of the forcing due to the doubling of carbon dioxide on climate (the “Charney” report). The concept was subsequently extended to a wide variety of agents beyond well-mixed greenhouse gases (WMGHGs; carbon dioxide, methane, nitrous oxide, and halocarbons) to short-lived species such as ozone. The WMO and IPCC international assessments began the important sequence of periodic evaluations and quantifications of the forcings by natural (solar irradiance changes and stratospheric aerosols resulting from volcanic eruptions) and a growing set of anthropogenic agents (WMGHGs, ozone, aerosols, land surface changes, contrails). From the 1990s to the present, knowledge and scientific confidence in the radiative agents acting on the climate system have proliferated. The conceptual basis of RF has also evolved as both our understanding of the way radiative forcing drives climate change and the diversity of the forcing mechanisms have grown. This has led to the current situation where “effective radiative forcing” (ERF) is regarded as the preferred practical definition of radiative forcing in order to better capture the link between forcing and global-mean surface temperature change. The use of ERF, however, comes with its own attendant issues, including challenges in its diagnosis from climate models, its applications to small forcings, and blurring of the distinction between rapid climate adjustments (fast responses) and climate feedbacks; this will necessitate further elaboration of its utility in the future. Global climate model simulations of radiative perturbations by various agents have established how the forcings affect other climate variables besides temperature (e.g., precipitation). The forcing–response linkage as simulated by models, including the diversity in the spatial distribution of forcings by the different agents, has provided a practical demonstration of the effectiveness of agents in perturbing the radiative energy balance and causing climate changes. The significant advances over the past half century have established, with very high confidence, that the global-mean ERF due to human activity since preindustrial times is positive (the 2013 IPCC assessment gives a best estimate of 2.3 W m−2, with a range from 1.1 to 3.3 W m−2; 90% confidence interval). Further, except in the immediate aftermath of climatically significant volcanic eruptions, the net anthropogenic forcing dominates over natural radiative forcing mechanisms. Nevertheless, the substantial remaining uncertainty in the net anthropogenic ERF leads to large uncertainties in estimates of climate sensitivity from observations and in predicting future climate impacts. The uncertainty in the ERF arises principally from the incorporation of the rapid climate adjustments in the formulation, the well-recognized difficulties in characterizing the preindustrial state of the atmosphere, and the incomplete knowledge of the interactions of aerosols with clouds. This uncertainty impairs the quantitative evaluation of climate adaptation and mitigation pathways in the future. A grand challenge in Earth system science lies in continuing to sustain the relatively simple essence of the radiative forcing concept in a form similar to that originally devised, and at the same time improving the quantification of the forcing. This, in turn, demands an accurate, yet increasingly complex and comprehensive, accounting of the relevant processes in the climate system.

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Schindler, Ralf-Dieter. "Proper Forcing and Remarkable Cardinals." Bulletin of Symbolic Logic 6, no. 2 (June 2000): 176–84. http://dx.doi.org/10.2307/421205.

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The present paper investigates the power of proper forcings to change the shape of the universe, in a certain well-defined respect. It turns out that the ranking among large cardinals can be used as a measure for that power. However, in order to establish the final result I had to isolate a new large cardinal concept, which I dubbed “remarkability.” Let us approach the exact formulation of the problem—and of its solution—at a slow pace.Breathtaking developments in the mid 1980s found one of its culminations in the theorem, due to Martin, Steel, and Woodin, that the existence of infinitely many Woodin cardinals with a measurable cardinal above them all implies that AD, the axiom of determinacy, holds in the least inner model containing all the reals, L(ℝ) (cf. [6[, p. 91). One of the nice things about AD is that the theory ZF + AD + V = L(ℝ) appears as a choiceless “completion” of ZF in that any interesting question (in particular, about sets of reals) seems to find an at least attractive answer in that theory (cf., for example, [5] Chap. 6). (Compare with ZF + V = L!) Beyond that, AD is very canonical as may be illustrated as follows.Let us say that L(ℝ) is absolute for set-sized forcings if for all posets P ∈ V, for all formulae ϕ, and for all ∈ ℝ do we have thatwhere is a name for the set of reals in the extension.

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Bottcher, Frits. "Climate Change: Forcing a Treaty." Energy & Environment 7, no. 4 (December 1996): 377–90. http://dx.doi.org/10.1177/0958305x9600700407.

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The theory of global warming, for which there is little evidence, has come to dominate the world's environmental agenda to such an extent that an international treaty is based on it. This remarkable feat came about through the well-orchestrated efforts of an inner circle of science-policy makers within the IPCC, who dominated discussion in order to achieve the necessary 'scientific consensus' for politicians to take action. This paper explains how all this was achieved, and traces the global warming campaign from its inception in the 1980s to the Berlin conference of 1995.

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Crook, N. Andrew, and Donna F. Tucker. "Flow over Heated Terrain. Part I: Linear Theory and Idealized Numerical Simulations." Monthly Weather Review 133, no. 9 (September 1, 2005): 2552–64. http://dx.doi.org/10.1175/mwr2964.1.

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Abstract The flow past heated topography is examined with both linear and nonlinear models. It is first shown that the forcing of an obstacle with horizontally homogenous surface heating can be approximated by the forcing of an obstacle with surface heating isolated over the obstacle. The small-amplitude flow past an obstacle with isolated heating is then examined with a linear model. Under the linear approximation, the flow response to heated topography is simply the addition of the separate responses to thermal and orographic forcing. These separate responses are first considered individually and then the combined response is examined. Nondimensional parameters are developed that measure the relative importance of thermal and orographic forcing. Nonaxisymmetric forcing is then considered by examining the flow along and across a heated elliptically shaped obstacle. It is shown that the low-level lifting is maximized when the flow is along the major axis of the obstacle. The linear solutions are then tested in a nonlinear anelastic model. The response to a heat source and orography are first examined separately. Good agreement is found between nonlinear and linear models for the individual responses to thermal and orographic forcing. The case of uniformly heated flow past an obstacle is then examined. In these simulations, the thermal response is isolated by subtracting the orographic-only response from the full thermal–orographic response. The numerical simulations are able to capture the main features of the thermal response. Finally, numerical simulations of the flow along and across an elliptically shaped heated obstacle are examined, where it is verified that the lifting is maximized when the flow is along the major axis of the obstacle. These results are extended in Part II of this study to examine the moist convective response to flow over both idealized terrain and the complex terrain of the Rocky Mountains of the United States.

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Ozaralli, Nurdan. "A Study on Conflict Resolution Styles Employed by Theory-X and Theory-Y Leaders and Perceived Leader Competence." Vision: The Journal of Business Perspective 6, no. 2 (July 2002): 81–86. http://dx.doi.org/10.1177/097226290200600208.

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The purpose of this study is to find out which conflict resolution strategies are preferred by Theory X (autocratic) and Theory Y (democratic) leaders in conflict situations. A sample of (n = 150) MBA students who work assessed their superiors' conflict resolution behavior by Howat and London's (1980) Conflict Resolution Strategies Instrument which identified five conflict resolution strategies – Confrontation, Withdrawal, Forcing, Smoothing, and Compromise. The students also assessed their superiors' leadership style on a scale as Theory X (autocratic) and Theory Y (democratic) leaders, as well as their effectiveness as leaders. In this study, mostly preferred conflict resolution strategies employed by autocratic and democratic leaders were identified. The findings of the study pointed out that High-X leaders were more confronting and forcing in resolving conflict compared to Low-X managers. Besides, they withdrew less from conflict situations. High-Y leaders, on the other hand, use confrontation, smoothing, and compromising styles in conflict situations significantly more often compared to Low-Y leaders. They use forcing and withdrawal less than Low-Y leaders. The three conflict resolution styles—confronting, compromising and smoothing were found to be good contributors of managerial competence. In addition, as managers were evaluated high on the Theory Y scale, the managerial competence perceptions of employees and their satisfaction with their supervisor increased.

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Bobok, Jozef. "Forcing relation on minimal interval patterns." Fundamenta Mathematicae 169, no. 2 (2001): 161–73. http://dx.doi.org/10.4064/fm169-2-5.

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Kunen, Kenneth. "Compact scattered spaces in forcing extensions." Fundamenta Mathematicae 185, no. 3 (2005): 261–66. http://dx.doi.org/10.4064/fm185-3-4.

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Zapletal, Jindřich. "Preserving P-points in definable forcing." Fundamenta Mathematicae 204, no. 2 (2009): 145–54. http://dx.doi.org/10.4064/fm204-2-4.

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Krueger, John. "Coherent adequate sets and forcing square." Fundamenta Mathematicae 224, no. 3 (2014): 279–300. http://dx.doi.org/10.4064/fm224-3-5.

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Rosłanowski, Andrzej, and Saharon Shelah. "The last forcing standing with diamonds." Fundamenta Mathematicae 246, no. 2 (2019): 109–59. http://dx.doi.org/10.4064/fm898-9-2018.

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Fuchs, Laszlo. "Forcing Linearity Numbers for Abelian Groups." Communications in Algebra 32, no. 5 (December 31, 2004): 1855–64. http://dx.doi.org/10.1081/agb-120029908.

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Sanwong, Jintana. "Forcing Linearity Numbers for Multiplication Modules." Communications in Algebra 34, no. 12 (December 2006): 4591–96. http://dx.doi.org/10.1080/00927870600936740.

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Maxson, C. J. "Forcing Linearity Numbers for Projective Modules." Journal of Algebra 251, no. 1 (May 2002): 1–11. http://dx.doi.org/10.1006/jabr.2001.9102.

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Journal articles on the topic 'Forcing theory'

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