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### Single Idea 10146

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

Full Idea

The Axiom of Choice is a pure existence statement, without defining conditions. It was necessary to provide a foundation for Cantor's theory of transfinite cardinals and ordinal numbers, but its nonconstructive character engendered heated controversy.

Gist of Idea

Cantor's theories needed the Axiom of Choice, but it has led to great controversy

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.43