13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Maddy on Zermelo] |
13039 | Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen] |
13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |