Kripke-Platek set theory: Difference between revisions
no edit summary
RhubarbJayde (talk | contribs) No edit summary |
RhubarbJayde (talk | contribs) No edit summary |
||
| (One intermediate revision by the same user not shown) | |||
Line 6:
* Axiom of induction: transfinite induction along the \(\in\)-relation (this implies the axiom of foundation)
* Axiom of empty set: There exists a set with no members.
* 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 infinity]]: there is an inductive set.
* 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 \(\forall x \in X \exists y \in Y \varphi(x,y)\).
| |||