Sinossi
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
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
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
Product Description
Comprehensive in its selection of topics and results, this self-contained text examines the relative strengths and the consequences of the axiom of choice. Subjects include consistency and independence, permutation models, and examples and counterexamples of the axiom's use. Each chapter contains several problems and concludes with some historical remarks. 1973 edition.
Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.
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Paperback. Condizione: new. Paperback. 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 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9780486466248
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