### Single Idea 13486

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation]

Full Idea

Zermelo assumes that not every predicate has an extension but rather that given a set we may separate out from it those of its members satisfying the predicate. This is called 'separation' (Aussonderung).

Gist of Idea

Not every predicate has an extension, but Separation picks the members that satisfy a predicate

Source

report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by William D. Hart - The Evolution of Logic 3

Book Reference

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.69

Related Idea

Idea 18105
Replacement enforces a 'limitation of size' test for the existence of sets **[Bostock]**