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For an overview of the Axiom of Choice see the Relevance of the Axiom of Choice (FAQ Launcher).
- Notation and Format
- Axiom of Choice Quiz
- Formal systems, axiomatic theories, and metatheory
- Euclidean geometry and the parallel postulate
- 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
- Axioms that imply AC
- The axiom of determinacy: An axiom which contradicts AC
- Category Theory: A new foundation of mathematics?
- Accept AC?
- ZFC Axioms
- Notation Index
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Last significant update ... a long time ago
Last tweak on May 27, 1997