Relevant bibliographies by topics / Dedekind cuts

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Dedekind cuts'

Author: Grafiati
Published: 4 June 2021
Last updated: 10 February 2022

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Journal articles on the topic "Dedekind cuts"

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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Dedekind cuts"

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Pimentel, Thiago Trindade. "Construção dos números reais via cortes de Dedekind." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-18102018-164352/.

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O objetivo desta dissertação é apresentar a construção dos números reais a partir de cortes de Dedekind. Para isso, vamos estudar os números naturais, os números inteiros, os números racionais e as propriedades envolvidas. Então, a partir dos números racionais, iremos construir o corpo dos números reais e estabelecer suas propriedades. Um corte de Dedekind, assim nomeado em homenagem ao matemático alemão Richard Dedekind, é uma partição dos números racionais em dois conjuntos não vazios A e B em que cada elemento de A é menor do que todos os elementos de B e A não contém um elemento máximo. Se
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Ribeiro, Fernando AraÃjo. "ConstruÃÃes dos nÃmeros reais voltadas para os professores da rede bÃsica de ensino." Universidade Federal do CearÃ, 2015. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=14671.

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CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior<br>Este trabalho tem como objetivo mostrar que o conjunto dos nÃmeros reais à um corpo ordenado completo e que, a menos de um isomorfismo, à Ãnico. Este trabalho à voltado para todos aqueles que tenham interesse em MatemÃtica, sobretudo, para os professores de MatemÃtica do ensino mÃdio que utilizam as propriedades do conjunto dos nÃmeros reais sem conhecer a teoria matemÃtica envolvida. Para tanto, à necessÃrio caracterizar o conjunto dos reais a fim de provar suas propriedades. Aqui, utilizamos duas construÃÃes, a saber: os reais via
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Silva, José Elias da. "A construção dos números reais e aplicações." Universidade Estadual da Paraíba, 2016. http://tede.bc.uepb.edu.br/jspui/handle/tede/2850.

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Submitted by Jean Medeiros (jeanletras@uepb.edu.br) on 2017-09-12T12:42:53Z No. of bitstreams: 1 PDF - José Elias da Silva.pdf: 9535482 bytes, checksum: 4f018a51c1e15736072db257c4b86319 (MD5)<br>Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2017-10-26T16:05:13Z (GMT) No. of bitstreams: 1 PDF - José Elias da Silva.pdf: 9535482 bytes, checksum: 4f018a51c1e15736072db257c4b86319 (MD5)<br>Made available in DSpace on 2017-10-26T16:05:13Z (GMT). No. of bitstreams: 1 PDF - José Elias da Silva.pdf: 9535482 bytes, checksum: 4f018a51c1e15736072db257c4b86319 (MD5) Previous i
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Duarte, Carlos Eduardo de Lima. "Conjuntos num?ricos." Universidade Federal do Rio Grande do Norte, 2013. http://repositorio.ufrn.br:8080/jspui/handle/123456789/17017.

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Made available in DSpace on 2014-12-17T15:27:44Z (GMT). No. of bitstreams: 1 CarlosELD_DISSERT.pdf: 699872 bytes, checksum: f940eba1822577b96cbd189eefe2a0d9 (MD5) Previous issue date: 2013-03-15<br>Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior<br>In this work, we present a text on the Sets Numerical using the human social needs as a tool for construction new numbers. This material is intended to present a text that reconciles the correct teaching of mathmatics and clarity needed for a good learning<br>Neste trabalho, elaboramos um texto sobre os Conjuntos Num?ricos, utilizando
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Queiroz, Fabiana Moura de. "Um estudo sobre construções dos Números Reais." Universidade Federal de Goiás, 2015. http://repositorio.bc.ufg.br/tede/handle/tede/4555.

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Submitted by Erika Demachki (erikademachki@gmail.com) on 2015-05-19T18:16:57Z No. of bitstreams: 2 Dissertação - Fabiana Moura de Queiroz - 2015.pdf: 3272912 bytes, checksum: bb75fba8c8a71a93692d37b8aa3ba9c2 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)<br>Approved for entry into archive by Erika Demachki (erikademachki@gmail.com) on 2015-05-19T18:18:56Z (GMT) No. of bitstreams: 2 Dissertação - Fabiana Moura de Queiroz - 2015.pdf: 3272912 bytes, checksum: bb75fba8c8a71a93692d37b8aa3ba9c2 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b863
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Pontes, Kerly Monroe. "Existência e Unicidade dos Números Reais via Cortes de Dedekind." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/7505.

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Submitted by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-05-27T12:50:34Z No. of bitstreams: 1 arquivototal.pdf: 643760 bytes, checksum: c6fc649a3682bb07bcc815ff2163eef4 (MD5)<br>Approved for entry into archive by Leonardo Americo (leonardo@sti.ufpb.br) on 2015-05-27T12:52:35Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 643760 bytes, checksum: c6fc649a3682bb07bcc815ff2163eef4 (MD5)<br>Made available in DSpace on 2015-05-27T12:52:35Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 643760 bytes, checksum: c6fc649a3682bb07bcc815ff2163eef4 (MD5) Previous issue date: 2014-08-29<
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Book chapters on the topic "Dedekind cuts"

1

Georgiev, Ivan. "Dedekind Cuts and Long Strings of Zeros in Base Expansions." In Lecture Notes in Computer Science. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-80049-9_23.

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2

Clawson, Calvin C. "Dedekind’s Cut." In The Mathematical Traveler. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-6014-6_10.

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3

"Appendix. MacNeille Order Completion Through Dedekind Cuts and Related Results." In Solution of Continuous Nonlinear PDEs Through Order Completion. Elsevier, 1994. http://dx.doi.org/10.1016/s0304-0208(08)71809-7.

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You might also be interested in the extended bibliographies on the topic 'Dedekind cuts' for particular source types:
Journal articles
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