翻訳と辞書 Words near each other ・ Forchristsake ・ Forcht Group of Kentucky ・ Forcht-Wade Correctional Center ・ Forchtenberg ・ Forchtenstein ・ Forchtenstein Castle ・ Forcible entry ・ Forcible Entry Act ・ Forcible Entry Act 1381 ・ Forcible Entry Act 1429 ・ Forcible Entry Act 1588 ・ Forcible Entry Act 1623 ・ Forcier ・ Forcing ・ Forcing (mathematics) ・ Forcing (recursion theory) ・ Forcing bid ・ Forcing defense ・ Forcing function ・ Forcing function (differential equations) ・ Forcing notrump ・ Forcing Out the Silence ・ Forcing pass ・ Forciolo ・ Forcipator ・ Forcipiger ・ Forcipiger longirostris ・ Forcipomyiinae ・ Forcipulatida ・ ForCIS 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 Forcing (recursion theory) ： ウィキペディア英語版 Forcing (recursion theory) Forcing in recursion theory is a modification of Paul Cohen's original set theoretic technique of forcing to deal with the effective concerns in recursion theory. Conceptually the two techniques are quite similar, in both one attempts to build generic objects (intuitively objects that are somehow 'typical') by meeting dense sets. Also both techniques are elegantly described as a relation (customarily denoted $\backslash Vdash$) between 'conditions' and sentences. However, where set theoretic forcing is usually interested in creating objects that meet every dense set of conditions in the ground model, recursion theoretic forcing only aims to meet dense sets that are arithmetically or hyperarithmetically definable. Therefore some of the more difficult machinery used in set theoretic forcing can be eliminated or substantially simplified when defining forcing in recursion theory. But while the machinery may be somewhat different recursion theoretic and set theoretic forcing are properly regarded as an application of the same technique to different classes of formulas. ==Terminology== In this article we use the following terminology. ;real: an element of $2^\backslash omega$. In other words a function that maps each integer to either 0 or 1. ;string: an element of $2^$. In other words a finite approximation to a real. ;notion of forcing: A notion of forcing is a set $P$ and a partial order on $P$, $\backslash succ\_$ with a ''greatest element'' $0\_$. ;condition: An element in a notion of forcing. We say a condition $p$ is stronger than a condition $q$ just when $q\; \backslash succ\_P\; p$. ;compatible conditions: Given conditions $p,q$ say that $p$ and $q$ are compatible if there is a condition $r$ with $p\; \backslash succ\_P\; r$ and $q\; \backslash succ\_P\; r$. ;$p\backslash mid\; q$: $p$ and $q$ are incompatible. ;Filter : A subset $F$ of a notion of forcing $P$ is a filter if $p,q\; \backslash in\; F\; \backslash implies\; p\; \backslash nmid\; q$ and $p\; \backslash in\; F\; \backslash land\; q\; \backslash succ\_P\; p\; \backslash implies\; q\; \backslash in\; F$. In other words a filter is a compatible set of conditions closed under weakening of conditions. ;Ultrafilter: A maximal filter, i.e., $F$ is an ultrafilter if $F$ is a filter and there is no filter $F\text{'}$ properly containing $F$ ;Cohen forcing: The notion of forcing $C$ where conditions are elements of $2^$ and $(\backslash tau\; \backslash succ\_C\; \backslash sigma\; \backslash iff\; \backslash sigma\; \backslash supset\; \backslash tau$) Note that for Cohen forcing $\backslash succ\_$ is the reverse of the containment relation. This leads to an unfortunate notational confusion where some recursion theorists reverse the direction of the forcing partial order (exchanging $\backslash succ\_P$ with $\backslash prec\_P$ which is more natural for Cohen forcing but is at odds with the notation used in set theory. 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「Forcing (recursion theory)」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.