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The axiom of choice /
Provability, Computability and Reflection.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam : New York :
North-Holland Pub. Co. ; American Elsevier Pub. Co.,
1973.
|
| Colección: | Studies in logic and the foundations of mathematics ;
v. 75. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo Texto completo |
MARC
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| 100 | 1 | |a Jech, Thomas J. | |
| 245 | 1 | 4 | |a The axiom of choice / |c Thomas J. Jech. |
| 260 | |a Amsterdam : |b North-Holland Pub. Co. ; |a New York : |b American Elsevier Pub. Co., |c 1973. | ||
| 300 | |a 1 online resource (xi, 202 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 Studies in logic and the foundations of mathematics ; |v v. 75 | |
| 504 | |a Includes bibliographical references. | ||
| 588 | 0 | |a Print version record. | |
| 506 | |3 Use copy |f Restrictions unspecified |2 star |5 MiAaHDL | ||
| 533 | |a Electronic reproduction. |b [Place of publication not identified] : |c HathiTrust Digital Library, |d 2011. |5 MiAaHDL | ||
| 538 | |a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |u http://purl.oclc.org/DLF/benchrepro0212 |5 MiAaHDL | ||
| 583 | 1 | |a digitized |c 2011 |h HathiTrust Digital Library |l committed to preserve |2 pda |5 MiAaHDL | |
| 505 | 0 | |a Front Cover; The Axiom of Choice; Copyright Page; Preface; Contents; Preface; Chapter 1. Introduction; 1.1. The Axiom of Choice; 1.2. A nonmeasurable set of real numbers; 1.3. A paradoxical decomposition of the sphere; 1.4. Problems; 1.5. Historical remarks; Chapter 2. Use of the Axiom of Choice; 2.1. Equivalents of the Axiom of Choice; 2.2. Some applications of the Axiom of Choice in mathematics; 2.3. The Prime Ideal Theorem; 2.4. The Countable Axiom of Choice; 2.5. Cardinal numbers; 2.6. Problems; 2.7. Historical remarks; Chapter 3. Consistency of the Axiom of Choice | |
| 505 | 8 | |a 3.1. Axiomatic systems and consistency3.2. Axiomatic set theory; 3.3. Transitive models of ZF; 3.4. The constructible universe; 3.5. Problems; 3.6. Historical remarks; Chapter 4. Permutation models; 4.1. Set theory with atoms; 4.2. Permutation models; 4.3. The basic Fraenkel model; 4.4. The second Fraenkel model; 4.5. The ordered Mostowski model; 4.6. Problems; 4.7. Historical remarks; Chapter 5. Independence of the Axiom of Choice; 5.1. Generic models; 5.2. Symmetric submodels of generic models; 5.3. The basic Cohen model; 5.4. The second Cohen model | |
| 505 | 8 | |a 5.5. Independence of the Axiom of Choice from the Ordering Principle5.6. Problems; 5.7. Historical remarks; Chapter 6. Embedding Theorems; 6.1. The First Embedding Theorem; 6.2. Refinements of the First Embedding Theorem; 6.3. Problems; 6.4. Historical remarks; Chapter 7. Models with finite supports; 7.1. Independence of the Axiom of Choice from the Prime Ideal Theorem; 7.2. Independence of the Prime Ideal Theorem from the Ordering Principle; 7.3. Independence of the Ordering Principle from the Axiom of Choice for Finite Sets; 7.4. The Axiom of Choice for Finite Sets; 7.5. Problems | |
| 505 | 8 | |a 7.6. Historical remarksChapter 8. Some weaker versions of the Axiom of Choice; 8.1. The Principle of Dependent Choices and its generalization; 8.2. Independence results concerning the Principle of Dependent Choices; 8.3. Problems; 8.4. Historical remarks; Chapter 9. Nontransferable statements; 9.1. Statements which imply AC in ZF but are weaker than AC in ZFA; 9.2. Independence results in ZFA; 9.3. Problems; 9.4. Historical remarks; Chapter 10. Mathematics without choice; 10.1. Properties of the real line; 10.2. Algebra without choice; 10.3. Problems; 10.4. Historical remarks | |
| 505 | 8 | |a Chapter 11. Cardinal numbers in set theory without choice11.1. Ordering of cardinal numbers; 11.2. Definability of cardinal numbers; 11.3. Arithmetic of cardinal numbers; 11.4. Problems; 11.5. Historical remarks; Chapter 12. Some properties contradicting the Axiom of Choice; 12.1. Measurability of N1; 12.2. Closed unbounded sets and partition properties; 12.3. The Axiom of Determinateness; 12.4. Problems; 12.5. Historical remarks; Appendix; A.1. Equivalents of the Axiom of Choice; A.2. Equivalents of the Prime Ideal Theorem; A.3. Various independence results; A.4. Miscellaneous examples | |
| 520 | |a Provability, Computability and Reflection. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Axiom of choice. | |
| 650 | 0 | |a Axioms. | |
| 650 | 0 | |a Mathematics |x Philosophy. | |
| 650 | 6 | |a Axiomes. |0 (CaQQLa)201-0040462 | |
| 650 | 6 | |a Math�ematiques |x Philosophie. |0 (CaQQLa)201-0000824 | |
| 650 | 6 | |a Axiome du choix. |0 (CaQQLa)201-0039740 | |
| 650 | 7 | |a MATHEMATICS |x Infinity. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Logic. |2 bisacsh | |
| 650 | 7 | |a Mathematics |x Philosophy |2 fast |0 (OCoLC)fst01012213 | |
| 650 | 7 | |a Axioms |2 fast |0 (OCoLC)fst00824492 | |
| 650 | 7 | |a Axiom of choice |2 fast |0 (OCoLC)fst00824488 | |
| 650 | 7 | |a Mengenlehre |2 gnd |0 (DE-588)4074715-3 | |
| 650 | 1 | 7 | |a Keuzeaxioma. |2 gtt |
| 650 | 7 | |a Teoria Dos Conjuntos. |2 larpcal | |
| 650 | 7 | |a Axiome du choix. |2 ram | |
| 776 | 0 | 8 | |i Print version: |a Jech, Thomas J. |t Axiom of choice. |d Amsterdam : North-Holland Pub. Co. ; New York : American Elsevier Pub. Co., 1973 |z 0444104844 |z 9780444104847 |w (DLC) 73075535 |w (OCoLC)772981 |
| 830 | 0 | |a Studies in logic and the foundations of mathematics ; |v v. 75. | |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/book/9780444104847 |z Texto completo |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/bookseries/0049237X/75 |z Texto completo |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/publication?issn=0049237X&volume=75 |z Texto completo |