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Single Idea 13647

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

Full Idea

The axiom of choice is essential for proving the downward Löwenheim-Skolem Theorem.

Gist of Idea

Choice is essential for proving downward Löwenheim-Skolem

Source

Stewart Shapiro (Foundations without Foundationalism [1991], 4.1)

Book Ref

Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.80