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Single Idea 15899

[from 'Understanding the Infinite' by Shaughan Lavine, in 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII ]

Full Idea

The Axiom of Replacement (of Skolem and Fraenkel) was remarkable for its universal acceptance, though it seemed to have no consequences except for the properties of the higher reaches of the Cantorian infinite.

Gist of Idea

Replacement was immediately accepted, despite having very few implications

Source

Shaughan Lavine (Understanding the Infinite [1994], I)

Book Reference

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.5


Related Ideas

Idea 15933 Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine]

Idea 15945 Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine]