Talk:Kripke–Platek set theory with urelements

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In what way does it differ from just ZF without the axiom of infinity ? -- 22:41, 26 Apr 2005 (UTC)Mike (Michel Josserand)

It lacks for instance axioms for power sets, an infinite set, or choice. Bgohla 22:48, 2005 May 3 (UTC)

If there's no infinity, the power set and the choice hold. I realize that the axiom of foundation is stated differently from it is in ZF but apparently ZF without infinity can be derived from KPU. Can KPU be derived from ZF minus infinity, in other words, does ZF actually preclude urelements? - Michel42

Compare & Contrast[edit]

Can somebody who's an expert in this topic write about how KPU differs from other axiomatizations? Statements like "KPU is considered freer than ZF" or "KPU is favoured by constructivists" or "XXXX famous result cannot be proved with KPU, but YYYYY famous result can." Crasshopper (talk) 07:15, 19 December 2010 (UTC)