The Axiom of Choice (Dover Books on Mathematics)

Table of Contents:
Preface1. Introduction2. Use of the axiom of choice3. Consistency of the axiom of choice4. Permutation models5. Independence of the axiom of choice6. Embedding theorems7. Models with finite supports8. Some weaker versions of the axiom of choice9. Nontransferable statements10. Mathematics without choice11. Cardinal numbers in set theory without choice12. Some properties contradicting the axiom of choiceAppendix 1. Equivalents of the axiom of choiceAppendix 2. Equivalents of the Prime Ideal TheoremAppendix 3. Various independence resultsAppendix 4. Miscellaneous examplesReferencesAuthor IndexSubject IndexList of Symbols

Marc Notes:
Originally published: Amsterdam: North-Holland Pub. Co.;New York: American Elsevier Pub. Co., 1973. Studies in logic and the foundations of mathematics, v. 75.

Biographical Note:
Thomas J. Jech is Professor Emeritus at Pennsylvania State University.

Publisher Marketing:
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