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### Single Idea 10148

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX]

Full Idea

Zermelo's Axiom of Choice asserts that for any set of non-empty sets that (pairwise) have no elements in common, then there is a set that 'simultaneously chooses' exactly one element from each set. Note that this is an existential claim.

Gist of Idea

Axiom of Choice: a set exists which chooses just one element each of any set of sets

Source

Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I)

Book Reference

Feferman,S/Feferman,A.B.: 'Alfred Tarski: life and logic' [CUP 2008], p.46

A Reaction

The Axiom is now widely accepted, after much debate in the early years. Even critics of the Axiom turn out to be relying on it.