The Axiom of Choice (Dover Books on Mathematics). Questo articolo non è disponibile.
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Lingua: inglese
Editore: Dover Publications, 2008
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- Titolo
- The Axiom of Choice (Dover Books on Mathematics)
- Autore
- Thomas J. Jech
- Editore
- Dover Publications
- Anno di pubblicazione
- 2008
- Condizione
- very_good
- Rilegatura
- Brossura
- Lingua
- inglese
- ISBN 10
- 0486466248
- ISBN 13
- 9780486466248
Comprehensive in its selection of topics and results, this self-contained text examines the relative strengths and consequences of the axiom of choice. Each chapter contains several problems, graded according to difficulty, and concludes with some historical remarks.
An introduction to the use of the axiom of choice is followed by explorations of consistency, permutation models, and independence. Subsequent chapters examine embedding theorems, models with finite supports, weaker versions of the axiom, and nontransferable statements. The final sections consider mathematics without choice, cardinal numbers in set theory without choice, and properties that contradict the axiom of choice, including the axiom of determinacy and related topics
An introduction to the use of the axiom of choice is followed by explorations of consistency, permutation models, and independence. Subsequent chapters examine embedding theorems, models with finite supports, weaker versions of the axiom, and nontransferable statements. The final sections consider mathematics without choice, cardinal numbers in set theory without choice, and properties that contradict the axiom of choice, including the axiom of determinacy and related topics
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Contenuti
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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