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.
AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom.
This book grew out of my interest in what is common to three disciplines: mathematics, philosophy, and history.
This book, Consequences of the Axiom of Choice, is a comprehensive listing of statements that have been proved in the last 100 years using the axiom of choice.
AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom.
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 ...
Equivalents of the Axiom of Choice
"This book chronicles the work of mathematician Ernst Zermelo (1871-1953) and his development of set theory's crucial principle, the axiom of choice.
We relate Freyd's topos-theoretic models for the independence of the axiom of choice to the more familiar symmetric Boolean-valued models.
Provability, Computability and Reflection
... Paterson–Fischer–Meyer paper: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.4249 Cook–Aanderaa paper: http://www.ams.org/journals/tran/1969-142-00/S0002-9947-1969-02492128/S0002-9947-1969-0249212-8.pdf Maass paper: ...