Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.
Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.
Preface 1. Introduction 2. Use of the axiom of choice 3. Consistency of the axiom of choice 4. Permutation models 5. Independence of the axiom of choice 6. Embedding theorems 7. Models with finite supports 8. Some weaker versions of the axiom of choice 9. Nontransferable statements 10. Mathematics without choice 11. Cardinal numbers in set theory without choice 12. Some properties contradicting the axiom of choice Appendix 1. Equivalents of the axiom of choice Appendix 2. Equivalents of the Prime Ideal Theorem Appendix 3. Various independence results Appendix 4. Miscellaneous examples References Author Index Subject Index List of Symbols
Preface 1. Introduction 2. Use of the axiom of choice 3. Consistency of the axiom of choice 4. Permutation models 5. Independence of the axiom of choice 6. Embedding theorems 7. Models with finite supports 8. Some weaker versions of the axiom of choice 9. Nontransferable statements 10. Mathematics without choice 11. Cardinal numbers in set theory without choice 12. Some properties contradicting the axiom of choice Appendix 1. Equivalents of the axiom of choice Appendix 2. Equivalents of the Prime Ideal Theorem Appendix 3. Various independence results Appendix 4. Miscellaneous examples References Author Index Subject Index List of Symbols
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