more from Shaughan Lavine

Single Idea 15945

[catalogued under 4. Formal Logic / F. Set Theory ST / 1. Set Theory]

Full Idea

Second-order set theory is just like first-order set-theory, except that we use the version of Replacement with a universal second-order quantifier over functions from set to sets.

Gist of Idea

Second-order set theory just adds a version of Replacement that quantifies over functions


Shaughan Lavine (Understanding the Infinite [1994], VII.4)

Book Reference

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.226

Related Idea

Idea 13034 Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen]