Relativized ordinal analysis: The case of Power Kripke–Platek set theory

The paper relativizes the method of ordinal analysis developed for Kripke–Platek set theory to theories which have the power set axiom. We show that it is possible to use this technique to extract information about Power Kripke–Platek set theory, KP(P)KP(P).As an application it is shown that whenever KP(P)+ACKP(P)+AC proves a Π2P statement then it holds true in the segment VτVτ of the von Neumann hierarchy, where τ stands for the Bachmann–Howard ordinal.