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Journal articles on the topic 'Iterated forcing'

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Published: 1 February 2025

Last updated: 25 July 2025

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1

Friedman, Sy D. "Iterated Class Forcing." Mathematical Research Letters 1, no. 4 (1994): 427–36. http://dx.doi.org/10.4310/mrl.1994.v1.n4.a3.

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2

Groszek, Marcia J. "Applications of iterated perfect set forcing." Annals of Pure and Applied Logic 39, no. 1 (1988): 19–53. http://dx.doi.org/10.1016/0168-0072(88)90044-9.

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3

Ferrero, Daniela, Thomas Kalinowski, and Sudeep Stephen. "Zero forcing in iterated line digraphs." Discrete Applied Mathematics 255 (February 2019): 198–208. http://dx.doi.org/10.1016/j.dam.2018.08.019.

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4

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

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5

Ihoda, Jaime I., and Saharon Shelah. "Souslin forcing." Journal of Symbolic Logic 53, no. 4 (1988): 1188–207. http://dx.doi.org/10.1017/s0022481200028012.

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AbstractWe define the notion of Souslin forcing, and we prove that some properties are preserved under iteration. We define a weaker form of Martin's axiom, namely , and using the results on Souslin forcing we show that is consistent with the existence of a Souslin tree and with the splitting number s = ℵ1. We prove that proves the additivity of measure. Also we introduce the notion of proper Souslin forcing, and we prove that this property is preserved under countable support iterated forcing. We use these results to show that ZFC + there is an inaccessible cardinal is equiconsistent with ZFC

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6

Audrito, Giorgio, and Matteo Viale. "Absoluteness via resurrection." Journal of Mathematical Logic 17, no. 02 (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: s

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7

Ishiu, Tetsuya, and Paul B. Larson. "Some results about (+) proved by iterated forcing." Journal of Symbolic Logic 77, no. 2 (2012): 515–31. http://dx.doi.org/10.2178/jsl/1333566635.

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AbstractWe shall show the consistency of CH+⌝(+) and CH+(+)+there are no club guessing sequences on ω1. We shall also prove that ◊+ does not imply the existence of a strong club guessing sequence on ω1.

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8

Shelah, Saharon. "Iterated forcing and normal ideals onω 1". Israel Journal of Mathematics 60, № 3 (1987): 345–80. http://dx.doi.org/10.1007/bf02780398.

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9

Mitchell, William. "Prikry forcing at κ+ and beyond". Journal of Symbolic Logic 52, № 1 (1987): 44–50. http://dx.doi.org/10.2307/2273859.

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If U is a normal measure on κ then we can add indiscernibles for U either by Prikry forcing [P] or by taking an iterated ultrapower which will add a sequence of indiscernibles for over M. These constructions are equivalent: the set C of indiscernibles for added by the iterated ultrapower is Prikry generic for [Mat]. Prikry forcing has been extended for sequences of measures of length by Magidor [Mag], and his method readily extends to . In this case the measure U is replaced by a sequence of measures and the set C of indiscernibles is replaced by a system of indiscernibles for : is a function

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10

Kanovei, Vladimir. "On non-wellfounded iterations of the perfect set forcing." Journal of Symbolic Logic 64, no. 2 (1999): 551–74. http://dx.doi.org/10.2307/2586484.

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AbstractWe prove that if I is a partially ordered set in a countable transitive model of ZFC then can be extended by a generic sequence of reals ai, i ∈ I, such that is preserved and every ai is Sacks generic over [〈aj: j < i〉]. The structure of the degrees of -constructibility of reals in the extension is investigated.As applications of the methods involved, we define a cardinal invariant to distinguish product and iterated Sacks extensions, and give a short proof of a theorem (by Budinas) that in ω2-iterated Sacks extension of L the Burgess selection principle for analytic equivalence rel

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11

Eisworth, Todd. "On iterated forcing for successors of regular cardinals." Fundamenta Mathematicae 179, no. 3 (2003): 249–66. http://dx.doi.org/10.4064/fm179-3-4.

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12

Tohmé, Fernando, Gianluca Caterina, and Jonathan Gangle. "Iterated Admissibility Through Forcing in Strategic Belief Models." Journal of Logic, Language and Information 29, no. 4 (2020): 491–509. http://dx.doi.org/10.1007/s10849-020-09317-4.

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13

Shelah, Saharon. "Some notes on iterated forcing with $2^{\aleph_0}>\aleph_2$." Notre Dame Journal of Formal Logic 29, no. 1 (1987): 1–17. http://dx.doi.org/10.1305/ndjfl/1093637766.

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14

Apter, Arthur W. "Some structural results concerning supercompact cardinals." Journal of Symbolic Logic 66, no. 4 (2001): 1919–27. http://dx.doi.org/10.2307/2694985.

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Abstract.We show how the forcing of [5] can be iterated so as to get a model containing supercompact cardinals in which every measurable cardinal δ is δ+ supercompact. We then apply this iteration to prove three additional theorems concerning the structure of the class of supercompact cardinals.

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15

Mohammadpour, Rahman. "New methods in forcing iteration and applications." Bulletin of Symbolic Logic 29, no. 2 (2023): 300–302. http://dx.doi.org/10.1017/bsl.2023.7.

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AbstractThe Theme. Strong forcing axioms like Martin’s Maximum give a reasonably satisfactory structural analysis of $H(\omega _2)$ . A broad program in modern Set Theory is searching for strong forcing axioms beyond $\omega _1$ . In other words, one would like to figure out the structural properties of taller initial segments of the universe. However, the classical techniques of forcing iterations seem unable to bypass the obstacles, as the resulting forcings axioms beyond $\omega _1$ have not thus far been strong enough! However, with his celebrated work on generalised side conditions, I. Ne

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16

Schlindwein, Chaz. "Shelah's work on non-semi-proper iterations, II." Journal of Symbolic Logic 66, no. 4 (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

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17

Metzler, Wolfgang. "Iterated Differentiable Maps with Nowhere Differentiable Basin Boundaries." Zeitschrift für Naturforschung A 48, no. 5-6 (1993): 669–72. http://dx.doi.org/10.1515/zna-1993-5-616.

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Abstract The fractal basin boundary of a two-dimensional discrete dynamical system modelling a chaotic forcing applied to bistability is shown to be identical to the graph of an infinite series F(x,t)= of weighted iterates of an ergodic unimodal interval function f. In the special case, when f is the logistic map in "full chaos", i.e. ƒ: x ↦ 4x(1 - x), F is a nowhere differentiable function of x for each t > exp(-λf) (even equal to the Weierstrass function), where λf >0 is denoting the Lyapunov exponent of f. For further chaotic functions f, nowhere-differentiability is shown to be obvio

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18

Mitchell, William J. "A Gitik iteration with nearly Easton factoring." Journal of Symbolic Logic 68, no. 2 (2003): 481–502. http://dx.doi.org/10.2178/jsl/1052669060.

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AbstractWe reprove Gitik's theorem that if the GCH holds and o(κ) = κ + 1 then there is a generic extension in which κ is still measurable and there is a closed unbounded subset C of κ such that every ν ∈ C is inaccessible in the ground model.Unlike the forcing used by Gitik, the iterated forcing ℛλ+1 used in this paper has the property that if λ is a cardinal less then κ then ℛλ+1 can be factored in V as ℛκ+1 = ℛλ+1 × ℛλ+1,κ where ∣ℛλ+1∣ ≤ λ+ and ℛλ+1,κ does not add any new subsets of λ.

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19

Dordal, Peter Lars. "A model in which the base-matrix tree cannot have cofinal branches." Journal of Symbolic Logic 52, no. 3 (1987): 651–64. http://dx.doi.org/10.1017/s0022481200029662.

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AbstractA model of ZFC is constructed in which the distributivity cardinal h is , and in which there are no ω2-towers in [ω]ω. As an immediate corollary, it follows that any base-matrix tree in this model has no cofinal branches. The model is constructed via a form of iterated Mathias forcing, in which a mixture of finite and countable supports is used.

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20

Wathan, F., R. Hoshyar, and R. Tafazolli. "Dynamic Grouped Chip-Level Iterated Multiuser Detection Based on Gaussian Forcing Technique." IEEE Communications Letters 12, no. 3 (2008): 167–69. http://dx.doi.org/10.1109/lcomm.2008.071931.

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21

Kanovei, Vladimir, and Vassily Lyubetsky. "On the Significance of Parameters in the Choice and Collection Schemata in the 2nd Order Peano Arithmetic." Mathematics 11, no. 3 (2023): 726. http://dx.doi.org/10.3390/math11030726.

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We make use of generalized iterations of the Sacks forcing to define cardinal-preserving generic extensions of the constructible universe L in which the axioms of ZF hold and in addition either (1) the parameter-free countable axiom of choice ACω* fails, or (2) ACω* holds but the full countable axiom of choice ACω fails in the domain of reals. In another generic extension of L, we define a set X⊆P(ω), which is a model of the parameter-free part PA2* of the 2nd order Peano arithmetic PA2, in which CA(Σ21) (Comprehension for Σ21 formulas with parameters) holds, yet an instance of Comprehension C

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22

DILÃO, RUI, and JOÃO GRACIANO. "EVALUATING DETERMINISTIC POLICIES IN TWO-PLAYER ITERATED GAMES." International Journal of Bifurcation and Chaos 19, no. 12 (2009): 4039–53. http://dx.doi.org/10.1142/s0218127409025213.

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We construct a statistical ensemble of games, wherein each independent subensemble we have two players playing the same game. We derive the mean payoffs per move of the representative players of the game, and we evaluate all the deterministic policies with finite memory. In particular, we show that if one of the players has a generalized tit-for-tat policy, the mean payoff per move of both players is the same, forcing the equalization of the mean payoffs per move. In the case of symmetric, noncooperative and dilemmatic games, we show that generalized tit-for-tat or imitation policies together

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23

Shelah, Saharon. "Two cardinal invariants of the continuum (∂<α) and FS linearly ordered iterated forcing". Acta Mathematica 192, № 2 (2004): 187–223. http://dx.doi.org/10.1007/bf02392740.

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24

Jockusch, Carl G., and Robert I. Soare. "Boolean algebras, Stone spaces, and the iterated Turing jump." Journal of Symbolic Logic 59, no. 4 (1994): 1121–38. http://dx.doi.org/10.2307/2275695.

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AbstractWe show, roughly speaking, that it requires ω iterations of the Turing jump to decode nontrivial information from Boolean algebras in an isomorphism invariant fashion. More precisely, if α is a recursive ordinal, is a countable structure with finite signature, and d is a degree, we say that has αth-jump degreed if d is the least degree which is the αth jump of some degree c such there is an isomorphic copy of with universe ω in which the functions and relations have degree at most c. We show that every degree d ≥ 0(ω) is the ωth jump degree of a Boolean algebra, but that for n < ω n

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25

Gitik, Moti. "On generic elementary embeddings." Journal of Symbolic Logic 54, no. 3 (1989): 700–707. http://dx.doi.org/10.2307/2274734.

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Suppose that I is a precipitous ideal over a cardinal κ and j is a generic embedding of I. What is the nature of j? If we assume the existence of a supercompact cardinal then, by Foreman, Magidor and Shelah [FMS], it is quite unclear where some of such j's are coming from. On the other hand, if ¬∃κ0(κ) = κ++, then, by Mitchell [Mi], the restriction of j to the core model is its iterated ultrapower by measures of it. A natural question arising here is if each iterated ultrapower of can be obtained as the restriction of a generic embedding of a precipitous ideal. Notice that there are obvious li

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26

Lee, Chia-Ying, Michael K. Tippett, Adam H. Sobel, and Suzana J. Camargo. "Autoregressive Modeling for Tropical Cyclone Intensity Climatology." Journal of Climate 29, no. 21 (2016): 7815–30. http://dx.doi.org/10.1175/jcli-d-15-0909.1.

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Abstract An autoregressive model is developed to simulate the climatological distribution of global tropical cyclone (TC) intensity. The model consists of two components: a regression-based deterministic component that advances the TC intensity in time and depends on the storm state and surrounding large-scale environment and a stochastic forcing. Potential intensity, deep-layer mean vertical shear, and midlevel relative humidity are the environmental variables included in the deterministic component. Given a storm track and its environment, the model is initialized and then iterated along the

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27

Rashidinia, Jalil, Mehri Sajjadian, Jorge Duarte, Cristina Januário, and Nuno Martins. "On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination Strategy." Complexity 2018 (December 2, 2018): 1–11. http://dx.doi.org/10.1155/2018/7191487.

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In this article, we consider the discretized classical Susceptible-Infected-Recovered (SIR) forced epidemic model to investigate the consequences of the introduction of different transmission rates and the effect of a constant vaccination strategy, providing new numerical and topological insights into the complex dynamics of recurrent diseases. Starting with a constant contact (or transmission) rate, the computation of the spectrum of Lyapunov exponents allows us to identify different chaotic regimes. Studying the evolution of the dynamical variables, a family of unimodal-type iterated maps wi

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28

Nord-Larsen, Thomas, Henrik Meilby, and Jens Peter Skovsgaard. "Simultaneous estimation of biomass models for 13 tree species: effects of compatible additivity requirements." Canadian Journal of Forest Research 47, no. 6 (2017): 765–76. http://dx.doi.org/10.1139/cjfr-2016-0430.

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A desirable feature of biomass models distinguishing different tree components is compatible additivity of the component functions. Due to forcing of parameter estimates, such additivity is achieved at an expense of precision of the component functions. This study aimed to analyse the loss of precision incurred by forcing of parameters in tree biomass models due to (i) additivity constraints, (ii) combining global and species-specific parameters, and (iii) estimating component functions simultaneously as a system instead of as individual equations. Based on biomass data from 697 trees includin

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29

Wei-Chiang, Wu. "Multiuser Resource Allocation Algorithms for Downlink OFDMA-based MIMO Network." International Journal of Engineering Research & Science 4, no. 3 (2018): 14–28. https://doi.org/10.5281/zenodo.1213531.

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<strong><em>Abstract</em></strong><strong>—</strong><em>The problem of simultaneous multiuser resource (subcarriers-and-bits) allocation algorithm in OFDMA-based multiple input-multiple output (MIMO) system has recently attracted significant interest. In this paper, we employ adaptive modulation technique and advanced use of multiple antennas at both the transmitter and receiver to develop four resource allocation schemes. The first scheme assigns subcarrier to the user with best channel gain and employs spatial multiplexing (SM) on the MIMO system to further enhance the throughput. The

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30

BAIYA, SUPARAT, and KASAMSUK UNGCHITTRAKOOL. "Modified inertial Mann’s algorithm and inertial hybrid." Carpathian Journal of Mathematics 39, no. 1 (2022): 27–43. http://dx.doi.org/10.37193/cjm.2023.01.02.

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"In this work, we introduce and study the modified inertial Mann’s algorithm and inertial hybrid algorithm for approximating some fixed points of a k-strict pseudo-contractive mapping in Hilbert spaces. Weak convergence to a solution of fixed-point problems for a k-strict pseudo-contractive mapping is obtained by using the modified inertial Mann’s algorithm. In order to obtain strong convergence, we introduce an inertial hybrid algorithm by using the inertial extrapolation method mixed with the convex combination of three iterated vectors and forcing for strong convergence by the hybrid projec

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31

Blass, Andreas. "Marcia J. Groszek. Applications of iterated perfect set forcing. Annals of pure and applied logic, vol. 39 (1988), pp. 19– 53." Journal of Symbolic Logic 55, no. 1 (1990): 360–61. http://dx.doi.org/10.2307/2274996.

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32

Beal, Aubrey N., and Robert N. Dean. "A Random Stimulation Source for Evaluating MEMS Devices using an Exact Solvable Chaotic Oscillator." Additional Conferences (Device Packaging, HiTEC, HiTEN, and CICMT) 2015, DPC (2015): 001594–625. http://dx.doi.org/10.4071/2015dpc-wp32.

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MEMS devices are nearly ubiquitous, with applications ranging from automobiles to toys, medical equipment to missiles, and cell phones to industrial equipment. At the microscale, fabrication tolerances are significantly less precise than at the scale of traditional machining techniques. This can result in significant differences in the operating characteristics between otherwise identical MEMS devices. A wide bandwidth random excitation source is ideal for evaluating these components, whether used as the forcing function for an electromechanical shaker employed to measure transmissibility, or

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33

LÜCKE, PHILIPP, RALF SCHINDLER та PHILIPP SCHLICHT. "Σ1(κ)-DEFINABLE SUBSETS OF H(κ+)". Journal of Symbolic Logic 82, № 3 (2017): 1106–31. http://dx.doi.org/10.1017/jsl.2017.36.

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AbstractWe study Σ1(ω1)-definable sets (i.e., sets that are equal to the collection of all sets satisfying a certain Σ1-formula with parameter ω1 ) in the presence of large cardinals. Our results show that the existence of a Woodin cardinal and a measurable cardinal above it imply that no well-ordering of the reals is Σ1(ω1)-definable, the set of all stationary subsets of ω1 is not Σ1(ω1)-definable and the complement of every Σ1(ω1)-definable Bernstein subset of ${}_{}^{{\omega _1}}\omega _1^{}$ is not Σ1(ω1)-definable. In contrast, we show that the existence of a Woodin cardinal is compatible

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34

Argyros, I. K. "Forcing sequences and inexact Newton iterates in Banach space." Applied Mathematics Letters 13, no. 1 (2000): 77–80. http://dx.doi.org/10.1016/s0893-9659(99)00148-2.

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35

Poveda, Alejandro. "Contributions to the Theory of Large Cardinals through the Method of Forcing." Bulletin of Symbolic Logic 27, no. 2 (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 th

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36

Claverie, Benjamin, and Ralf Schindler. "Increasing u2 by a stationary set preserving forcing." Journal of Symbolic Logic 74, no. 1 (2009): 187–200. http://dx.doi.org/10.2178/jsl/1231082308.

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AbstractWe show that if I is a precipitous ideal on ω1 and if θ > ω1 is a regular cardinal, then there is a forcing ℙ = ℙ(I, θ) which preserves the stationarity of all I-positive sets such that in Vℙ, ⟨Hθ; ∈, I⟩ is a generic iterate of a countable structure ⟨M; ∈, Ī⟩. This shows that if the nonstationary ideal on ω1 is precipitous and exists, then there is a stationary set preserving forcing which increases . Moreover, if Bounded Martin's Maximum holds and the nonstationary ideal on ω1 is precipitous, then .

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37

Argyros, I. K. "Relations Between Forcing Sequences and Inexact Newton Iterates in Banach Space." Computing 63, no. 2 (1999): 131–44. http://dx.doi.org/10.1007/s006070050055.

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38

Argyros, Ioannis K. "Relations between forcing sequences and inexact newton-like iterates in banach space." International Journal of Computer Mathematics 71, no. 2 (1999): 235–46. http://dx.doi.org/10.1080/00207169908804804.

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39

Si, Jian-Guo, and Sui Sun Cheng. "Smooth solutions of a nonhomogeneous iterative functional differential equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 4 (1998): 821–31. http://dx.doi.org/10.1017/s0308210500021806.

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This paper is concerned with an iterative functional differential equation x(t) = c1x(t) + c2x[2](t) + … cmχ[m](t) + F(t), where x[i](t) is the i-th iterate of the function x(t). By means of Schauder's Fixed Point Theorem, we establish a local existence theorem for smooth solutions which also depend continuously on the forcing function F(t).

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40

Kellner, Jakob, and Saharon Shelah. "Saccharinity." Journal of Symbolic Logic 76, no. 4 (2011): 1153–83. http://dx.doi.org/10.2178/jsl/1318338844.

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AbstractWe present a method to iterate finitely splitting lim-sup tree forcings along non-wellfounded linear orders. As an application, we introduce a new method to force (weak) measurability of all definable sets with respect to a certain (non-ccc) ideal.

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41

Wang, Peiguang, and Xiang Liu. "Rapid Convergence for Telegraph Systems with Periodic Boundary Conditions." Journal of Function Spaces 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/1982568.

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The generalized quasilinearization method is applied in this paper to a telegraph system with periodic boundary conditions. We consider the case in which the forcing function F(t,x,U) satisfies the following condition: ∂n-1F(t,x,U)/∂Un-1 exists and is quasimonotone nondecreasing or nonincreasing. We develop nonlinear iterates of order n-1 which will be different with n being even or odd. Finally, we develop two sequences which converge to the solution of the telegraph system and the convergence is of order n.

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42

Andres, Jan. "Randomized Sharkovsky-type theorems and their application to random impulsive differential equations and inclusions on tori." Stochastics and Dynamics 19, no. 05 (2019): 1950036. http://dx.doi.org/10.1142/s0219493719500369.

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Our randomized versions of the Sharkovsky-type cycle coexistence theorems on tori and, in particular, on the circle are applied to random impulsive differential equations and inclusions. The obtained effective coexistence criteria for random subharmonics with various periods are formulated in terms of the Lefschetz numbers (in dimension one, in terms of degrees) of the impulsive maps and their iterates w.r.t. the (deterministic) state variables. Otherwise, the forcing properties of certain periods of the given random subharmonics are employed, provided there exists a random harmonic solution.

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43

Chang, Edmund K. M. "An Idealized Nonlinear Model of the Northern Hemisphere Winter Storm Tracks." Journal of the Atmospheric Sciences 63, no. 7 (2006): 1818–39. http://dx.doi.org/10.1175/jas3726.1.

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Abstract In this paper, a nonlinear dry model, forced by fixed radiative forcing alone, has been constructed to simulate the Northern Hemisphere winter storm tracks. A procedure has been devised to iterate the radiative equilibrium temperature profile such that at the end of the iterations the model climate closely resembles the desired target climate. This iterative approach is applied to simulate the climatological storm tracks in January. It is found that, when the three-dimensional temperature distribution in the model resembles the observed distribution, the model storm tracks are much to

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44

Britto, Abraham Benjamin, and Sathesh Mariappan. "Lock-in phenomenon of vortex shedding in oscillatory flows: an analytical investigation pertaining to combustors." Journal of Fluid Mechanics 872 (June 7, 2019): 115–46. http://dx.doi.org/10.1017/jfm.2019.353.

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An analytical investigation is performed to understand the lock-in phenomenon, observed in vortex shedding combustors. Several aeroengine afterburners and ramjets use a bluff body to stabilize the flame. The bluff body sheds vortices. During the occurrence of high-amplitude combustion instability, the frequency of vortex shedding locks in to the frequency of the chamber acoustic field. This phenomenon is termed vortex-acoustic lock-in. In general, there is a two-way coupling between the vortex shedding process and the acoustic field, making analytical investigation difficult. Since the frequen

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45

Lewis, Christian. "Anthony Trollope's Formal Experiment: Repetition and the Anti-romantic Marriage Plot." Novel: A Forum on Fiction 57, no. 1 (2024): 67–85. http://dx.doi.org/10.1215/00295132-11052367.

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Abstract In Miss Mackenzie, Anthony Trollope attempted to write a marriage plot without love or romance but admitted that he was unable to do so. This essay argues that Trollope's formal experiment developing the “anti-romantic” marriage plot did not end with Miss Mackenzie but continued across eighteen novels written from 1864 to 1876. The essay performs a midrange reading of this set of novels to argue that across this experiment Trollope iterates his anti-romantic marriage plot, replicating his central conflict and establishing three stock characters (moral maidens, hesitating heroines, and

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Dobrinen, Natasha. "James Cummings and Ernest Schimmerling, editors. Lecture Note Series of the London Mathematical Society, vol. 406. Cambridge University Press, New York, xi + 419 pp. - Paul B. Larson, Peter Lumsdaine, and Yimu Yin. An introduction to Pmax forcing. pp. 5–23. - Simon Thomas and Scott Schneider. Countable Borel equivalence relations. pp. 25–62. - Ilijas Farah and Eric Wofsey. Set theory and operator algebras. pp. 63–119. - Justin Moore and David Milovich. A tutorial on set mapping reflection. pp. 121–144. - Vladimir G. Pestov and Aleksandra Kwiatkowska. An introduction to hyperlinear and sofic groups. pp. 145–185. - Itay Neeman and Spencer Unger. Aronszajn trees and the SCH. pp. 187–206. - Todd Eisworth, Justin Tatch Moore, and David Milovich. Iterated forcing and the Continuum Hypothesis. pp. 207–244. - Moti Gitik and Spencer Unger. Short extender forcing. pp. 245–263. - Alexander S. Kechris and Robin D. Tucker-Drob. The complexity of classification problems in ergodic theory. pp. 265–299. - Menachem Magidor and Chris Lambie-Hanson. On the strengths and weaknesses of weak squares. pp. 301–330. - Boban Veličković and Giorgio Venturi. Proper forcing remastered. pp. 331–362. - Asger ToÖrnquist and Martino Lupini. Set theory and von Neumann algebras. pp. 363–396. - W. Hugh Woodin, Jacob Davis, and Daniel RodrÍguez. The HOD dichotomy. pp. 397–419." Bulletin of Symbolic Logic 20, no. 1 (2014): 94–97. http://dx.doi.org/10.1017/bsl.2014.1.

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Eklof, Paul C. "Fred Appenzeller. An independence result in quadratic form theory: infinitary combinatorics applied to ε-Hermitian spaces. The journal of symbolic logic, vol. 54 (1989), pp. 689–699. - Otmar Spinas. Linear topologies on sesquilinear spaces of uncountable dimension. Fundamenta mathematicae, vol. 139 (1991), pp. 119–132. - James E. Baumgartner, Matthew Foreman, and Otmar Spinas. The spectrum of the Γ-invariant of a bilinear space. Journal of algebra, vol. 189 (1997), pp. 406–418. - James E. Baumgartner and Otmar Spinas. Independence and consistency proofs in quadratic form theory. The journal of symbolic logic, vol. 56 (1991), pp. 1195–1211. - Otmar Spinas. Iterated forcing in quadratic form theory. Israel journal of mathematics, vol. 79 (1992), pp. 297–315. - Otmar Spinas. Cardinal invariants and quadratic forms. Set theory of the reals, edited by Haim Judah, Israel mathematical conference proceedings, vol. 6, Gelbart Research Institute for Mathematical Sciences, Bar-Ilan University, Ramat-Gan 1993, distributed by the American Mathematical Society, Providence, pp. 563–581. - Saharon Shelah and Otmar Spinas. Gross spaces. Transactions of the American Mathematical Society, vol. 348 (1996), pp. 4257–4277." Bulletin of Symbolic Logic 7, № 2 (2001): 285–86. http://dx.doi.org/10.2307/2687785.

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Corazza, Paul. "Forcing with Non-wellfounded Models." Australasian Journal of Logic 5 (November 30, 2007). http://dx.doi.org/10.26686/ajl.v5i0.1784.

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We develop the machinery for performing forcing over an arbitrary (possibly non-wellfounded) model of set theory. For consistency results, this machinery is unnecessary since such results can always be legitimately obtained by assuming that the ground model is (countable) transitive. However, for establishing properties of a given (possibly non-wellfounded) model, the fully developed machinery of forcing as a means to produce new related models can be useful. We develop forcing through iterated forcing, paralleling the standard steps of presentation found in [19] and [14].

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Bakke Haga, Karen, David Schrittesser, and Asger Törnquist. "Maximal almost disjoint families, determinacy, and forcing." Journal of Mathematical Logic, May 10, 2021, 2150026. http://dx.doi.org/10.1142/s0219061321500264.

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We study the notion of [Formula: see text]-MAD families where [Formula: see text] is a Borel ideal on [Formula: see text]. We show that if [Formula: see text] is any finite or countably iterated Fubini product of the ideal of finite sets [Formula: see text], then there are no analytic infinite [Formula: see text]-MAD families, and assuming Projective Determinacy and Dependent Choice there are no infinite projective [Formula: see text]-MAD families; and under the full Axiom of Determinacy + [Formula: see text] or under [Formula: see text] there are no infinite [Formula: see text]-mad families.

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Krishnamurthy, Deepak, and Manu Prakash. "Emergent programmable behavior and chaos in dynamically driven active filaments." Proceedings of the National Academy of Sciences 120, no. 28 (2023). http://dx.doi.org/10.1073/pnas.2304981120.

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How the behavior of cells emerges from their constituent subcellular biochemical and physical parts is an outstanding challenge at the intersection of biology and physics. A remarkable example of single-cell behavior occurs in the ciliate Lacrymaria olor , which hunts for its prey via rapid movements and protrusions of a slender neck, many times the size of the original cell body. The dynamics of this cell neck is powered by a coat of cilia across its length and tip. How a cell can program this active filamentous structure to produce desirable behaviors like search and homing to a target remai

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