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Artículos de revistas sobre el tema "Dedekind cuts"

Autor: Grafiati
Publicado: 4 de junio de 2021
Última modificación: 10 de febrero de 2022

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1

Dăneţ, Nicolae. "Dedekind cuts in C(X)." Banach Center Publications 95 (2011): 287–97. http://dx.doi.org/10.4064/bc95-0-16.

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2

Ehrlich, P. "Dedekind cuts of Archimedean complete ordered abelian groups." Algebra Universalis 37, no. 2 (1997): 223–34. http://dx.doi.org/10.1007/s000120050014.

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3

Fornasiero, Antongiulio, and Marcello Mamino. "Arithmetic of Dedekind cuts of ordered Abelian groups." Annals of Pure and Applied Logic 156, no. 2-3 (2008): 210–44. http://dx.doi.org/10.1016/j.apal.2008.05.001.

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4

Trujillo, Timothy. "Ramsey for R1 ultrafilter mappings and their Dedekind cuts." Mathematical Logic Quarterly 61, no. 4-5 (2015): 263–73. http://dx.doi.org/10.1002/malq.201300078.

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5

Tressl, Marcus. "Model completeness of o-minimal structures expanded by Dedekind cuts." Journal of Symbolic Logic 70, no. 1 (2005): 29–60. http://dx.doi.org/10.2178/jsl/1107298509.

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§1. Introduction. Let M be a totally ordered set. A (Dedekind) cut p of M is a couple (pL, pR) of subsets pL, pR of M such that pL ⋃ pR = M and pL < pR, i.e., a < b for all a ∈ pL, b ∈ pR. In this article we are looking for model completeness results of o-minimal structures M expanded by a set pL for a cut p of M. This means the following. Let M be an o-minimal structure in the language L and suppose M is model complete. Let D be a new unary predicate and let p be a cut of (the underlying ordered set of) M. Then we are looking for a natural, definable expansion of the L(D)-structure (M,
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6

Tressl, Marcus. "The elementary theory of Dedekind cuts in polynomially bounded structures." Annals of Pure and Applied Logic 135, no. 1-3 (2005): 113–34. http://dx.doi.org/10.1016/j.apal.2004.12.003.

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7

BAUER, ANDREJ, and PAUL TAYLOR. "The Dedekind reals in abstract Stone duality." Mathematical Structures in Computer Science 19, no. 4 (2009): 757–838. http://dx.doi.org/10.1017/s0960129509007695.

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Abstract Stone Duality (ASD) is a direct axiomatisation of general topology, in contrast to the traditional and all other contemporary approaches, which rely on a prior notion of discrete set, type or object of a topos.ASD reconciles mathematical and computational viewpoints, providing an inherently computable calculus that does not sacrifice key properties of real analysis such as compactness of the closed interval. Previous theories of recursive analysis failed to do this because they were based on points; ASD succeeds because, like locale theory and formal topology, it is founded on the alg
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8

Crosilla, Laura, Hajime Ishihara, and Peter Schuster. "On constructing completions." Journal of Symbolic Logic 70, no. 3 (2005): 969–78. http://dx.doi.org/10.2178/jsl/1122038923.

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AbstractThe Dedekind cuts in an ordered set form a set in the sense of constructive Zermelo–Fraenkel set theory. We deduce this statement from the principle of refinement, which we distill before from the axiom of fullness. Together with exponentiation, refinement is equivalent to fullness. None of the defining properties of an ordering is needed, and only refinement for two–element coverings is used.In particular, the Dedekind reals form a set: whence we have also refined an earlier result by Aczel and Rathjen, who invoked the full form of fullness. To further generalise this, we look at Rich
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9

Chernikov, Artem, and Saharon Shelah. "ON THE NUMBER OF DEDEKIND CUTS AND TWO-CARDINAL MODELS OF DEPENDENT THEORIES." Journal of the Institute of Mathematics of Jussieu 15, no. 4 (2015): 771–84. http://dx.doi.org/10.1017/s1474748015000018.

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For an infinite cardinal ${\it\kappa}$, let $\text{ded}\,{\it\kappa}$ denote the supremum of the number of Dedekind cuts in linear orders of size ${\it\kappa}$. It is known that ${\it\kappa}<\text{ded}\,{\it\kappa}\leqslant 2^{{\it\kappa}}$ for all ${\it\kappa}$ and that $\text{ded}\,{\it\kappa}<2^{{\it\kappa}}$ is consistent for any ${\it\kappa}$ of uncountable cofinality. We prove however that $2^{{\it\kappa}}\leqslant \text{ded}(\text{ded}(\text{ded}(\text{ded}\,{\it\kappa})))$ always holds. Using this result we calculate the Hanf numbers for the existence of two-cardinal models with
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10

Höhle, Ulrich. "Fuzzy real numbers as Dedekind cuts with respect to a multiple-valued logic." Fuzzy Sets and Systems 24, no. 3 (1987): 263–78. http://dx.doi.org/10.1016/0165-0114(87)90027-3.

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11

Moniri, Mojtaba. "On definable completeness for ordered fields." Reports on Mathematical Logic 54 (2019): 95–100. http://dx.doi.org/10.4467/20842589rm.19.005.10653.

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We show that there are 0-definably complete ordered fields which are not real closed. Therefore, the theory of definably with parameters complete ordered fields does not follow from the theory of 0-definably complete ordered fields. The mentioned completeness notions for ordered fields are the definable versions of completeness in the sense of Dedekind cuts. In earlier joint work, we had shown that it would become successively weakened if we just required nonexistence of definable regular gaps and then disallowing parameters. The result in this note shows reducing in the opposite order, at lea
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12

Alves, Francisco Regis Vieira, and Marlene Alves Dias. "An Historical Investigation about the Dedekind´s Cuts: Some Implications for the Teaching of Mathematics in Brazil." Acta Didactica Napocensia 11, no. 3-4 (2018): 13–34. http://dx.doi.org/10.24193/adn.11.3-4.2.

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13

Coquand, Thierry, Sara Sadocco, Giovanni Sambin, and Jan M. Smith. "Formal topologies on the set of first-order formulae." Journal of Symbolic Logic 65, no. 3 (2000): 1183–92. http://dx.doi.org/10.2307/2586694.

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The completeness proof for first-order logic by Rasiowa and Sikorski [13] is a simplification of Henkin's proof [7] in that it avoids the addition of infinitely many new individual constants. Instead they show that each consistent set of formulae can be extended to a maximally consistent set, satisfying the following existence property: if it contains (∃x)ϕ it also contains some substitution ϕ(y/x) of a variable y for x. In Feferman's review [5] of [13], an improvement, due to Tarski, is given by which the proof gets a simple algebraic form.Sambin [16] used the same method in the setting of fo
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14

Brungs, H. H., and M. Schröder. "Prime Segments of Skew Fields." Canadian Journal of Mathematics 47, no. 6 (1995): 1148–76. http://dx.doi.org/10.4153/cjm-1995-059-3.

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AbstractAn additive subgroup P of a skew field F is called a prime of F if P does not contain the identity, but if the product xy of two elements x and y in F is contained in P, then x or y is in P. A prime segment of F is given by two neighbouring primes P1 ⊃ P2; such a segment is invariant, simple, or exceptional depending on whether A(P1) = {a ∈ P1 | P1aP1 ⊂ P1} equals P1, P2 or lies properly between P1 and P2. The set T(F) of all primes of F together with the containment relation is a tree if |T(F)| is finite, and 1 < |T(F)| < ∞ is possible if F is not commutative. In this paper we c
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15

Hoover, Douglas N. "A probabilistic interpolation theorem." Journal of Symbolic Logic 50, no. 3 (1985): 708–13. http://dx.doi.org/10.2307/2274325.

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The probability logic is a logic with a natural interpretation on probability spaces (thus, a logic whose model theory is part of probability theory rather than a system for putting probabilities on formulas of first order logic). Its exact definition and basic development are contained in the paper [3] of H. J. Keisler and the papers [1] and [2] of the author. Building on work in [2], we prove in this paper the following probabilistic interpolation theorem for .Let L be a countable relational language, and let A be a countable admissible set with ω ∈ A (in this paper some probabilistic notati
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16

van Dalen, Dirk. "Hermann Weyl's Intuitionistic Mathematics." Bulletin of Symbolic Logic 1, no. 2 (1995): 145–69. http://dx.doi.org/10.2307/421038.

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Dedicated to Dana Scott on his sixtieth birthday.It is common knowledge that for a short while Hermann Weyl joined Brouwer in his pursuit of a revision of mathematics according to intuitionistic principles. There is, however, little in the literature that sheds light on Weyl's role and in particular on Brouwer's reaction to Weyl's allegiance to the cause of intuitionism. This short episode certainly raises a number of questions: what made Weyl give up his own program, spelled out in “Das Kontinuum”, how did Weyl come to be so well-informed about Brouwer's new intuitionism, in what respect did
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17

Voss, Daniela. "Deleuze's Third Synthesis of Time." Deleuze Studies 7, no. 2 (2013): 194–216. http://dx.doi.org/10.3366/dls.2013.0102.

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Deleuze's theory of time set out in Difference and Repetition is a complex structure of three different syntheses of time – the passive synthesis of the living present, the passive synthesis of the pure past and the static synthesis of the future. This article focuses on Deleuze's third synthesis of time, which seems to be the most obscure part of his tripartite theory, as Deleuze mixes different theoretical concepts drawn from philosophy, Greek drama theory and mathematics. Of central importance is the notion of the cut, which is constitutive of the third synthesis of time defined as an a pri
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18

Zahid, Shekh, and Prasanta Ray. "On Closure Properties of Irrational and Transcendental Numbers under Addition and Multiplication." Volume 13, Issue 3 13, no. 3 (2016). http://dx.doi.org/10.33697/ajur.2016.026.

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In the article 'There are Truth and Beauty in Undergraduate Mathematics Research’, the author posted a problem regarding the closure properties of irrational and transcendental numbers under addition and multiplication. In this study, we investigate the problem using elementary mathematical methods and provide a new approach to the closure properties of irrational numbers. Further, we also study the closure properties of transcendental numbers. KEYWORDS: Irrational numbers; Transcendental numbers; Dedekind cuts; Algebraic numbers
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