more from Penelope Maddy

### Single Idea 18193

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII]

Full Idea

In the presence of other axioms, the Axiom of Foundation is equivalent to the claim that every set is a member of some Vα.

Clarification

A Vα is a stage of the hierarchy

Gist of Idea

The Axiom of Foundation says every set exists at a level in the set hierarchy

Source

Penelope Maddy (Naturalism in Mathematics [1997], I.3)

Book Reference

Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.60