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The logical foundations of mathematics /
The Logical Foundations of Mathematics.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Burlington :
Pergamon Press/Elsevier Science,
[2014], ©1982.
|
| Colección: | Foundations & philosophy of science & technology.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000Mi 4500 | ||
|---|---|---|---|
| 001 | EBOOKCENTRAL_ocn898771755 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
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| 020 | |a 9781483189635 |q (electronic bk.) | ||
| 020 | |a 1483189635 |q (electronic bk.) | ||
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| 035 | |a (OCoLC)898771755 | ||
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| 049 | |a UAMI | ||
| 100 | 1 | |a Hatcher, William S. | |
| 245 | 1 | 4 | |a The logical foundations of mathematics / |c by William S. Hatcher. |
| 260 | |a Burlington : |b Pergamon Press/Elsevier Science, |c [2014], ©1982. | ||
| 300 | |a 1 online resource (331 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 Foundations and philosophy of science and technology | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Front Cover; The Logical Foundations of Mathematics; Copyright Page; Dedication; Preface; Table of Contents; Chapter 1. First-order Logic; 1.1. The sentential calculus; 1.2. Formalization; 1.3. The statement calculus as a formal system; 1.4. First-order theories; 1.5. Models of first-order theories; 1.6. Rules of logic; natural deduction; 1.7. First-order theories with equality; variable-binding term operators; 1.8. Completeness with vbtos; 1.9. An example of a first-order theory; Chapter 2. The Origin of Modern Foundational Studies; 2.1. Mathematics as an independent science. | |
| 505 | 8 | |a 2.2. The arithmetization of analysis2.3. Constructivism; 2.4. Frege and the notion of a formal system; 2.5. Criteria for foundations; Chapter 3. Frege's System and the Paradoxes; 3,1. The intuitive basis of Frege's system; 3.2. Frege's system; 3.3. The theorem of infinity; 3.4. Criticisms of Frege's system; 3.5. The paradoxes; 3.6. Brouwer and intuitionism; 3.7. Poincare'snotion of im predicative definition; 3.8. Russell's principle of vicious circle; 3.9. The logical paradoxes and the semantic paradoxes; Chapter 4. The Theory of Types; 4.1. Quantifying predicate letters. | |
| 505 | 8 | |a 4.2. Predicative type theory4.3. The development of mathematics in PT; 4.4. The system TT; 4.5. Criticisms of type theory as a foundation for mathematics; 4.6. The system ST; 4.7. Type theory and first-order logic; Chapter 5. Zermelo-Fraenkel Set Theory; 5.1. Formalization of ZF; 5.2. The completing axioms; 5.3. Relations, functions, and simple recursion; 5.4. The axiom of choice; 5.5. The continuum hypothesis; descriptive set theory; 5.6. The systems of vonNeumann-Bernays-Godel and Mostowski-Kelley-Morse; 5.7. Number systems; ordinal recursion; 5.8. Conway's numbers. | |
| 505 | 8 | |a Chapter 6. Hilbert's Program and Godel's IncompletenessTheorems6.1. Hilbert's program; 6.2. Godel's theorems and their import; 6.3. The method of proof of Godel's theorems; recursive functions; 6.4. Nonstandard models of S; Chapter 7. The Foundational Systems of W.V. Quine; 7.1. The system NF; 7.2. Cantor's theorem in NF; 7.3. The axiom of choice in NF and the theorem of infinity; 7.4. NF and ST; typical ambiguity; 7.5. Quine's system ML; 7.6. Further results on NF; variant systems; 7.7. Conclusions; Chapter 8. Categorical Algebra; 8.1. The notion of a category. | |
| 505 | 8 | |a 8.2. The first-order language of categories8.3. Category theory and set theory; 8.4. Functors and large categories; 8.5. Formal development of the language and theory CS; 8.6. Topos theory; 8.7. Global elements in toposes; 8.8. Image factorizations and the axiom of choice; 8.9. A last look at CS; 8.10. ZF andWT; 8.11. The internal logic of toposes; 8.12. The internal language of a topos; 8.13. Conclusions; Selected Bibliography; Index. | |
| 520 | |a The Logical Foundations of Mathematics. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Mathematics |x Philosophy. | |
| 650 | 6 | |a Mathématiques |x Philosophie. | |
| 650 | 7 | |a MATHEMATICS |x Essays. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Pre-Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Reference. |2 bisacsh | |
| 650 | 7 | |a Mathematics |x Philosophy |2 fast | |
| 700 | 1 | |a Bunge, Mario. | |
| 758 | |i has work: |a The logical foundations of mathematics (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFvGt6FbHHRCYq8cctg83P |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Hatcher, William S. |t Logical Foundations of Mathematics : Foundations and Philosophy of Science and Technology Series. |d Burlington : Elsevier Science, ©2014 |z 9780080258003 |
| 830 | 0 | |a Foundations & philosophy of science & technology. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1901360 |z Texto completo |
| 938 | |a EBL - Ebook Library |b EBLB |n EBL1901360 | ||
| 938 | |a EBSCOhost |b EBSC |n 931370 | ||
| 994 | |a 92 |b IZTAP | ||