Hersteller der Reproduktion:
[S.l.]: HathiTrust Digital Library
Reproduktionsnotiz:
Online-Ausg. [S.l.] : HathiTrust Digital Library
Entstehung:
Anmerkungen:
Includes bibliographical references. - Print version record
Print version record
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
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
Beschreibung:
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
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
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
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
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