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THE
AXIOM

For an overview of the Axiom of Choice see the Relevance of the Axiom of Choice (FAQ Launcher).
 Introduction
 Notation and Format
 Philosophy
 Overview
 Axiom of Choice Quiz
 Foundations
 Formal systems, axiomatic theories, and metatheory
 Euclidean geometry and the parallel postulate
 ZFC
 Quiz Solutions and Weak Forms of AC
 Explanation of Quiz Answers
 Weak forms of AC
 Some theorems whose proofs within ZFC require Countable Choice or Dependent Choice
 Common Equivalents of AC
 Choice Principles, Ordering Principles, and Maximality Principles
 Less Well Known Equivalents of AC
 Cardinality Theorems
 Tychonoff's Theorem
 Every vectory space has a basis
 Theorems Whose Proofs Within ZFC Require AC
 Equivalents of the Ultrafilter Theorem
 A discontinuous additive function
 "Bad" sets of reals
 Conclusion
 Axioms that imply AC
 The axiom of determinacy: An axiom which contradicts AC
 Category Theory: A new foundation of mathematics?
 Accept AC?
 Appendix
 ZFC Axioms
 Notation Index
 Glossary
 Bibliography
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19921997
Infinite Ink
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Nancy McGough Last significant update ... a long time ago Last tweak on May 27, 1997 
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