Kripke-Platek set theory: Difference between revisions
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RhubarbJayde (talk | contribs) (Created page with "Kripke-Platek set theory, commonly abbreviated KP, is a weak foundation of set theory used to define admissible ordinals, which are immensely important in ordinal analysis and \(\alpha\)-recursion theory. In terms of proof-theoretic strength, its proof-theoretic ordinal is the BHO, and it is thus intermediate between \(\mathrm{ATR}_0\) and \(\Pi^1_1 \mathrm{-CA}_0\). The axioms of KP are...") |
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The axioms of KP are the following:
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* 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.
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