Kripke-Platek set theory: Difference between revisions

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* Axiom of induction: transfinite induction along the \(\in\)-relation (this implies the axiom of foundation)
* 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 empty set: There exists a set with no members.
* Axiom of pairing: If x, y are sets, then so is {x, y}.
* 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 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 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 \(\Delta_0\)-separation: Given any set \(X\) and any \(\Delta_0\)-formula \(\varphi(x)\), \(\{x \in X: \varphi(x)\}\) is also a set.
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