Kripke-Platek set theory: Difference between revisions

* Axiom of pairing: If \(x\), \(y\) are sets, then so is \(\{x, y\}\).

* Axiom of union: For any set \(x\), there is a set \(y\) such that the elements of \(y\) are precisely the elements of the elements of \(x\).

* Axiom of \(\Delta_0\)-separation: Given any set \(X\) and any \(\Delta_0\)-formula \(\varphi(x)\), \(\{x \in X: \varphi(x)\}\) is also a set.

* Axiom of \(\Delta_0\)-collection: If \(\varphi(x,y)\) is a \(\Delta_0\)-formula so that \(\forall x \exists y \varphi(x,y)\), then for all \(X\), there is some \(Y\) so that \(\forall x \in X \exists y \in Y \varphi(x,y)\).