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Set Theory, Arithmetic, and Foundations of Mathematics : Theorems, Philosophies.
A collection of remarkable papers from various areas of mathematical logic, written by outstanding members of the field.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2011.
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| Colección: | Lecture Notes in Logic, 36.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Kennedy, Juliette. | |
| 245 | 1 | 0 | |a Set Theory, Arithmetic, and Foundations of Mathematics : |b Theorems, Philosophies. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2011. | ||
| 300 | |a 1 online resource (243 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Lecture Notes in Logic, 36 ; |v v. 36 | |
| 505 | 0 | |a Cover; Title; Copyright; Dedication; Contents; Introduction; Historical remarks on Suslin's problem; 1. Suslin's problem.; 2. Consistency of ƠSH.; 3. Consistency of SH.; 4. Envoi.; REFERENCES; The continuum hypothesis, the generic-multiverse of sets, and the O conjecture; 1. A tale of two problems; 2. The generic-multiverse of sets.; 3. O-log; 4. The O conjecture.; 5. The complexity of O-logic.; 6. The weak multiverse laws and H(c+).; 7. Conclusions.; 8. Appendix.; REFERENCES;?-models of finite set theory; 1. Introduction.; 2. Preliminaries.; 3. Building?-models. | |
| 505 | 8 | |a 4. Models with special properties. 5. ZFfin and PA are not bi-interpretable.; 6. Concluding remarks and open questions.; REFERENCES; Tennenbaum's theorem for models of arithmetic; 1. Some historical background.; 2. Tennenbaum's theorem.; 3. Diophantine problems.; REFERENCES; Hierarchies of subsystems of weak arithmetic; 1. Introduction.; 2. Preliminaries.; 3. The main results.; 3.1. Proof of Theorem A; 3.2. Proof of Theorem B.; 3.3. Proofs of Theorems C and D.; REFERENCES; Diophantine correct open induction; Introduction.; Background. | |
| 505 | 8 | |a Wilkie's theorems and the models of Berarducci and Otero. 1. Axioms for DOI.; 2. Diophantine correct rings of Puiseux polynomials; 3. Generalized polynomials.; Special sequences of polynomials.; Theorems on generalized polynomials.; 4. A Class of Diophantine correct ordered rings.; REFERENCES; Tennenbaum's theorem and recursive reducts; 0. Conventions.; 1. Rich theories.; 2. Thin theories.; 3. Examples.; 4. Some 1-thin theories.; 5. More about LO.; REFERENCES; History of constructivism in the 20th century; 1. Introduction.; 2. Finitism.; 2.1. Finitist mathematics.; 2.2. Actualism. | |
| 505 | 8 | |a 3. Predicativism and semi-intuitionism. 3.1. Poincaré.; 3.2. The semi-intuitionists.; 3.3. Borel and the continuum.; 3.4. Weyl.; 4. Brouwerian intuitionism.; 4.1. Early period.; 4.2. Weak counterexamples and the creative subject.; 4.3. Brouwer's programme.; 5. Intuitionistic logic and arithmetic.; 5.1. L.E.J. Brouwer and intuitionistic logic.; 5.2. The Brouwer-Heyting-Kolmogorov interpretation.; 5.3. Formal intuitionistic logic and arithmetic through 1940.; 5.4. Metamathematics of intuitionistic logic and arithmetic after 1940.; 5.5. Formulas-as-types. | |
| 505 | 8 | |a 6. Intuitionistic analysis and stronger theories. 6.1. Choice sequences in Brouwer's writings.; 6.2. Axiomatization of intuitionistic analysis.; 6.3. The model theory of intuitionistic analysis.; 7. Constructive recursive mathematics.; 7.1. Classical recursive mathematics.; 7.2. Constructive recursive mathematics.; 8. Bishop's constructivism.; 8.1. Bishop's constructive mathematics.; 8.2. The relation of BCM to INT and CRM.; 9. Concluding remarks.; REFERENCES; A very short history of ultrafinitism; 1. Introduction:; 2. Short history and prehistory of ultrafinitism.; 2.1. Murios. | |
| 500 | |a 2.2. Apeiron. | ||
| 520 | |a A collection of remarkable papers from various areas of mathematical logic, written by outstanding members of the field. | ||
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Set theory. | |
| 650 | 0 | |a Logic, Symbolic and mathematical. | |
| 650 | 0 | |a Mathematics |x Philosophy. | |
| 650 | 6 | |a Théorie des ensembles. | |
| 650 | 6 | |a Logique symbolique et mathématique. | |
| 650 | 6 | |a Mathématiques |x Philosophie. | |
| 650 | 7 | |a MATHEMATICS |x Logic. |2 bisacsh | |
| 650 | 7 | |a Logic, Symbolic and mathematical |2 fast | |
| 650 | 7 | |a Mathematics |x Philosophy |2 fast | |
| 650 | 7 | |a Set theory |2 fast | |
| 700 | 1 | |a Kossak, Roman. | |
| 776 | 0 | 8 | |i Print version: |a Kennedy, Juliette. |t Set Theory, Arithmetic, and Foundations of Mathematics : Theorems, Philosophies. |d Cambridge : Cambridge University Press, ©2011 |z 9781107008045 |
| 830 | 0 | |a Lecture Notes in Logic, 36. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=803003 |z Texto completo |
| 880 | 0 | |6 505-00/(S |a Cover -- Title -- Copyright -- Dedication -- Contents -- Introduction -- Historical remarks on Suslin's problem -- 1. Suslin's problem. -- 2. Consistency of ¬SH. -- 3. Consistency of SH. -- 4. Envoi. -- REFERENCES -- The continuum hypothesis, the generic-multiverse of sets, and the Ω conjecture -- 1. A tale of two problems -- 2. The generic-multiverse of sets. -- 3. Ω-log -- 4. The Ω conjecture. -- 5. The complexity of Ω-logic. -- 6. The weak multiverse laws and H(c+). -- 7. Conclusions. -- 8. Appendix. -- REFERENCES -- ω-models of finite set theory -- 1. Introduction. -- 2. Preliminaries. -- 3. Building ω-models. -- 4. Models with special properties. -- 5. ZFfin and PA are not bi-interpretable. -- 6. Concluding remarks and open questions. -- REFERENCES -- Tennenbaum's theorem for models of arithmetic -- 1. Some historical background. -- 2. Tennenbaum's theorem. -- 3. Diophantine problems. -- REFERENCES -- Hierarchies of subsystems of weak arithmetic -- 1. Introduction. -- 2. Preliminaries. -- 3. The main results. -- 3.1. Proof of Theorem A -- 3.2. Proof of Theorem B. -- 3.3. Proofs of Theorems C and D. -- REFERENCES -- Diophantine correct open induction -- Introduction. -- Background. -- Wilkie's theorems and the models of Berarducci and Otero. -- 1. Axioms for DOI. -- 2. Diophantine correct rings of Puiseux polynomials -- 3. Generalized polynomials. -- Special sequences of polynomials. -- Theorems on generalized polynomials. -- 4. A Class of Diophantine correct ordered rings. -- REFERENCES -- Tennenbaum's theorem and recursive reducts -- 0. Conventions. -- 1. Rich theories. -- 2. Thin theories. -- 3. Examples. -- 4. Some 1-thin theories. -- 5. More about LO. -- REFERENCES -- History of constructivism in the 20th century -- 1. Introduction. -- 2. Finitism. -- 2.1. Finitist mathematics. -- 2.2. Actualism. | |
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