翻訳と辞書 Words near each other ・ Kripal Singh Shekhawat ・ Kripalu Center ・ Kripalu Maharaj ・ Kripalvananda ・ Kripamayee Kali Temple ・ Kripan ・ Kripapureeswarar Temple ・ Kripashankar Singh ・ Kripasur Sherpa ・ Kripekapura ・ Kripik ・ Kripke ・ Kripke semantics ・ Kripke structure (model checking) ・ Kripke–Platek set theory ・ Kripke–Platek set theory with urelements ・ Kripo live ・ Kripp Johnson ・ Kripparrian ・ Krippen station ・ Krippenbach ・ Krippendorf's Tribe ・ Krippendorf-Dittman Company ・ Krippendorff's alpha ・ Kripplebush Historic District ・ Krippner ・ Krips ・ Krirk University ・ Kris ・ Kris (disambiguation) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Kripke–Platek set theory with urelements ： ウィキペディア英語版 Kripke–Platek set theory with urelements The Kripke–Platek set theory with urelements (KPU) is an axiom system for set theory with urelements, based on the traditional (urelement-free) Kripke-Platek set theory. It is considerably weaker than the (relatively) familiar system ZFU. The purpose of allowing urelements is to allow large or high-complexity objects (such as the set of all reals) to be included in the theory's transitive models without disrupting the usual well-ordering and recursion-theoretic properties of the constructible universe; KP is so weak that this is hard to do by traditional means. ==Preliminaries== The usual way of stating the axioms presumes a two sorted first order language $L^$ * with a single binary relation symbol $\backslash in$. Letters of the sort $p,q,r,...$ designate urelements, of which there may be none, whereas letters of the sort $a,b,c,...$ designate sets. The letters $x,y,z,...$ may denote both sets and urelements. The letters for sets may appear on both sides of $\backslash in$, while those for urelements may only appear on the left, i.e. the following are examples of valid expressions: $p\backslash in\; a$, $b\backslash in\; a$. The statement of the axioms also requires reference to a certain collection of formulae called $\backslash Delta\_0$-formulae. The collection $\backslash Delta\_0$ consists of those formulae that can be built using the constants, $\backslash in$, $\backslash neg$, $\backslash wedge$, $\backslash vee$, and bounded quantification. That is quantification of the form $\backslash forall\; x\; \backslash in\; a$ or $\backslash exists\; x\; \backslash in\; a$ where $a$ is given set. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kripke–Platek set theory with urelements」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.