Editing Kripke–Platek set theory (section)

=== Comparison with Zermelo-Fraenkel set theory ===
As noted, the above are weaker than ZFC as they exclude the [[power set axiom]], choice, and sometimes infinity. Also the axioms of separation and collection here are weaker than the corresponding axioms in ZFC because the formulas φ used in these are limited to bounded quantifiers only.

The axiom of induction in the context of KP is stronger than the usual [[axiom of regularity]], which amounts to applying induction to the complement of a set (the class of all sets not in the given set).