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The axiom of choice / Thomas J. Jech

Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Studies in logic and the foundations of mathematics ; v. 75Publisher: Amsterdam ; New York : North-Holland Pub. Co, 2011Description: Online Ressource (xi, 202 pages)ISBN:
  • 9780444104847
  • 9780080954851
  • 0080954855
  • 0444104844
  • 0720422000
  • 0720422752
  • 9780444104847
  • 9780720422757
Subject(s): Additional physical formats: 0444104844 | 0720422000 | 0720422752 | Erscheint auch als: Axiom of choice. Druck-Ausgabe Amsterdam : North-Holland Pub. Co. ; New York : American Elsevier Pub. Co, 1973DDC classification:
  • Symbolic logic. Axiom of choice
  • 511.3
MSC: MSC: 03E25LOC classification:
  • QA248
Online resources: Additional physical formats: Online-Ausg. [S.l.] : HathiTrust Digital LibrarySummary: 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 modelSummary: 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. ProblemsSummary: 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 remarksSummary: 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 examplesSummary: 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 ChoiceSummary: Provability, Computability and ReflectionPPN: PPN: 878888470Package identifier: Produktsigel: BSZ-33-EBS-C1UB | BSZ-33-EBS-HSAA | GBV-33-EBS-MRI | GBV-33-EBS-ZHB | GBV-33-Freedom-BL | ZDB-1-ELC | ZDB-33-EBS | ZDB-33-ESD
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Online-Ausg. [S.l.] : HathiTrust Digital Library

Online-Ausg. [S.l.] : HathiTrust Digital Library. Online-Ausg. [S.l.] : HathiTrust Digital Library

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.

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