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

Set Forms. The Well-Ordering Theorem. The Axiom of Choice. The Law of the Trichotomy. Maximal Principles. Forms Equivalent to the Axiom of Choice Under the Axioms of Extensionality and Foundation. Algebraic Forms. Cardinal Number Forms. Forms from Topology, Analysis and Logic. Class Forms. The Well-Ordering Theorem. The Axiom of Choice. Maximal Principles. List of the Set Forms. List of the Class Forms. List of Forms Related to the Axiom of Choice. Bibliography. Index.


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© 1985
North Holland
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Reviews exhaustive survey... the second edition of this book is considerably thicker than the first... It is likely to be the standard reference work on this topic for some time to come. @source:Journal of Symbolic Logic