Equivalents of the Axiom of Choice II (Studies in Logic and the Foundations of Mathematics, Vol. 116) (Studies in Logic and the Foundations of Mathematics, Volume 116)

This monograph contains a selection of over 250 propositions which are equivalent to AC. The first part on set forms has sections on the well-ordering theorem, variants of AC, the law of the trichotomy, maximal principles, statements related to the axiom of foundation, forms from algebra, cardinal number theory, and a final section of forms from topology, analysis and logic. The second part deals with the axiom of choice for classes - well-ordering theorem, choice and maximal principles. Table of Contents......Page 8 Introduction......Page 9 Preliminary Definitions and Theorems......Page 12 1. The Well-Ordering Theorem......Page 26 2. The Axiom of Choice......Page 32 3. The Law of the Trichotomy......Page 46 4. Maximal Principles......Page 55 5. Forms Equivalent to the Axiom of Choice Under the Axioms of Extensionality and Foundation......Page 97 6. Algebraic Forms......Page 116 7. Cardinal Number Forms......Page 160 8. Forms from Topology, Analysis and Logic......Page 185 Part II. Class Forms......Page 207 1. The Well-Ordering Theorem......Page 209 2. The Axiom of Choice......Page 213 3. Maximal Principles......Page 224 List of the Set Forms......Page 268 List of the Class Forms......Page 290 List of Forms Related to the Axiom of Choice......Page 298 Bibliography......Page 307 Index of Authors......Page 323 Index of Symbols......Page 329 Index of Technical Terms......Page 332