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Academic literature on the topic 'Extensions compactes'

Author: Grafiati

Published: 14 December 2024

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Journal articles on the topic "Extensions compactes"

1

Casanovas, Enrique. "Compactly expandable models and stability." Journal of Symbolic Logic 60, no. 2 (1995): 673–83. http://dx.doi.org/10.2307/2275857.

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In analogy to ω-logic, one defines M-logic for an arbitrary structure M (see [5],[6]). In M-logic only those structures are considered in which a special part, determined by a fixed unary predicate, is isomorphic to M. Let L be the similarity type of M and T its complete theory. We say that M-logic is κ-compact if it satisfies the compactness theorem for sets of < κ sentences. In this paper we introduce the related notion of compactness for expandability: a model M is κ-compactly expandable if for every extension T′ ⊇ T of cardinality < κ, if every finite subset of T′ can be satisfied in an expansion of M, then T′ can also be satisfied in an expansion of M. Moreover, M is compactly expandable if it is ∥M∥+-compactly expandable. It turns out that M-logic is κ-compact iff M is κ-compactly expandable.Whereas for first-order logic consistency and finite satisfiability are the same, consistency with T and finite satisfiability in M are, in general, no longer the same thing. We call the model Mκ-expandable if every consistent extension T′ ⊇ T of cardinality < κ can be satisfied in an expansion of M. We say that M is expandable if it is ∥M∥+-expandable. Here we study the relationship between saturation, expandability and compactness for expandability. There is a close parallelism between our results about compactly expandable models and some theorems of S. Shelah about expandable models, which are in fact expressed in terms of categoricity of PC-classes (see [7, Th. VI.5.3, VI.5.4 and VI.5.5]). Our results could be obtained directly from these theorems of Shelah if expandability and compactness for expandability were the same notion.

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2

Caicedo, Xavier. "A simple solution to Friedman's fourth problem." Journal of Symbolic Logic 51, no. 3 (1986): 778–84. http://dx.doi.org/10.2307/2274031.

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AbstractIt is shown that Friedman's problem, whether there exists a proper extension of first order logic satisfying the compactness and interpolation theorems, has extremely simple positive solutions if one considers extensions by generalized (finitary) propositional connectives. This does not solve, however, the problem of whether such extensions exist which are also closed under relativization of formulas.

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3

Zhang, Zhihua. "Approximation of Bivariate Functions via Smooth Extensions." Scientific World Journal 2014 (2014): 1–16. http://dx.doi.org/10.1155/2014/102062.

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For a smooth bivariate function defined on a general domain with arbitrary shape, it is difficult to do Fourier approximation or wavelet approximation. In order to solve these problems, in this paper, we give an extension of the bivariate function on a general domain with arbitrary shape to a smooth, periodic function in the whole space or to a smooth, compactly supported function in the whole space. These smooth extensions have simple and clear representations which are determined by this bivariate function and some polynomials. After that, we expand the smooth, periodic function into a Fourier series or a periodic wavelet series or we expand the smooth, compactly supported function into a wavelet series. Since our extensions are smooth, the obtained Fourier coefficients or wavelet coefficients decay very fast. Since our extension tools are polynomials, the moment theorem shows that a lot of wavelet coefficients vanish. From this, with the help of well-known approximation theorems, using our extension methods, the Fourier approximation and the wavelet approximation of the bivariate function on the general domain with small error are obtained.

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4

van den Berg, Benno, and Ieke Moerdijk. "The axiom of multiple choice and models for constructive set theory." Journal of Mathematical Logic 14, no. 01 (2014): 1450005. http://dx.doi.org/10.1142/s0219061314500056.

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We propose an extension of Aczel's constructive set theory CZF by an axiom for inductive types and a choice principle, and show that this extension has the following properties: it is interpretable in Martin-Löf's type theory (hence acceptable from a constructive and generalized-predicative standpoint). In addition, it is strong enough to prove the Set Compactness theorem and the results in formal topology which make use of this theorem. Moreover, it is stable under the standard constructions from algebraic set theory, namely exact completion, realizability models, forcing as well as more general sheaf extensions. As a result, methods from our earlier work can be applied to show that this extension satisfies various derived rules, such as a derived compactness rule for Cantor space and a derived continuity rule for Baire space. Finally, we show that this extension is robust in the sense that it is also reflected by the model constructions from algebraic set theory just mentioned.

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5

Kim, Yong-Chan, and S. E. Abbas. "Some good extensions of compactness." Journal of Korean Institute of Intelligent Systems 13, no. 5 (2003): 614–20. http://dx.doi.org/10.5391/jkiis.2003.13.5.614.

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6

Enayat, Ali. "Conservative extensions of models of set theory and generalizations." Journal of Symbolic Logic 51, no. 4 (1986): 1005–21. http://dx.doi.org/10.2307/2273912.

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An attempt to answer the following question gave rise to the results of the present paper. Let be an arbitrary model of set theory. Does there exist an elementary extension of satisfying the two requirements: (1) contains an ordinal exceeding all the ordinals of ; (2) does not enlarge any (hyper) integer of ? Note that a trivial application of the ordinary compactness theorem produces a model satisfying condition (1); and an internal ultrapower modulo an internal ultrafilter produces a model satisfying condition (2) (but not (1), because of the axiom of replacement). Also, such a satisfying both conditions (1) and (2) exists if the external cofinality of the ordinals of is countable, since by [KM], would then have an elementary end extension.Using a class of models constructed by M. Rubin using in [RS], and already employed in [E1], we prove that our question in general has a negative answer (see Theorem 2.3). This result generalizes the results of M. Kaufmann and the author (appearing respectively in [Ka] and [E1]) concerning models of set theory with no elementary end extensions.In the course of the proof it was necessary to establish that all conservative extensions (see Definition 2.1) of models of ZF must be cofinal. This is in direct contrast with the case of Peano arithmetic where all conservative extensions are end extensional (as observed by Phillips in [Ph1]). This led the author to introduce two useful weakenings of the notion of a conservative end extension which, as shown by the “completeness” theorems in §3, can exist.

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7

Paúl, Pedro J. "New applications of Pták's extension theorem to weak compactness." Czechoslovak Mathematical Journal 39, no. 3 (1989): 454–58. http://dx.doi.org/10.21136/cmj.1989.102316.

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8

Gasparis, I. "An extension of James's compactness theorem." Journal of Functional Analysis 268, no. 1 (2015): 194–209. http://dx.doi.org/10.1016/j.jfa.2014.10.021.

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9

Aygün, Halis, A. Arzu Bural, and S. R. T. Kudri. "Fuzzy Inverse Compactness." International Journal of Mathematics and Mathematical Sciences 2008 (2008): 1–9. http://dx.doi.org/10.1155/2008/436570.

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We introduce definitions of fuzzy inverse compactness, fuzzy inverse countable compactness, and fuzzy inverse Lindelöfness on arbitrary -fuzzy sets in -fuzzy topological spaces. We prove that the proposed definitions are good extensions of the corresponding concepts in ordinary topology and obtain different characterizations of fuzzy inverse compactness.

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10

Pal, Arupkumar. "Regularity of operators on essential extensions of the compacts." Proceedings of the American Mathematical Society 128, no. 9 (2000): 2649–57. http://dx.doi.org/10.1090/s0002-9939-00-05611-2.

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