The Kripke–Platek axioms of set theory (KP) are a system of axioms for axiomatic set theory developed by Saul Kripke and Richard Platek. The axiom system, written in first-order logic, has an infinite number of axioms because an infinite axiom schema is used. KP is weaker than Zermelo–Fraenkel set theory (ZFC). Unlike ZFC, KP does not include the powerset axiom, and KP includes only limited forms of the axiom of separation and axiom of replacement from ZFC.

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  • The Kripke–Platek axioms of set theory (KP) are a system of axioms for axiomatic set theory developed by Saul Kripke and Richard Platek. The axiom system, written in first-order logic, has an infinite number of axioms because an infinite axiom schema is used. KP is weaker than Zermelo–Fraenkel set theory (ZFC). Unlike ZFC, KP does not include the powerset axiom, and KP includes only limited forms of the axiom of separation and axiom of replacement from ZFC. These restrictions on the axioms of KP lead to close connections between KP, generalized recursion theory, and the theory of admissible ordinals.
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  • The Kripke–Platek axioms of set theory (KP) are a system of axioms for axiomatic set theory developed by Saul Kripke and Richard Platek. The axiom system, written in first-order logic, has an infinite number of axioms because an infinite axiom schema is used. KP is weaker than Zermelo–Fraenkel set theory (ZFC). Unlike ZFC, KP does not include the powerset axiom, and KP includes only limited forms of the axiom of separation and axiom of replacement from ZFC.
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  • Kripke–Platek set theory
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