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00:00:45 1 The axioms of KP
00:03:42 2 Proof that Cartesian products exist
00:08:24 3 Admissible sets
00:08:57 4 See also



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"There is only one good, knowledge, and one evil, ignorance."
- Socrates



SUMMARY
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The Kripke–Platek axioms of set theory (KP), pronounced , are a system of axiomatic set theory developed by Saul Kripke and Richard Platek.
KP is considerably weaker than Zermelo–Fraenkel set theory (ZFC), and can be thought of as roughly the predicative part of ZFC. The consistency strength of KP with an axiom of infinity is given by the Bachmann–Howard ordinal. Unlike ZFC, KP does not include the power set 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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