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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Craig's theorem ： ウィキペディア英語版 Craig's theorem In mathematical logic, Craig's theorem states that any recursively enumerable set of well-formed formulas of a first-order language is (primitively) recursively axiomatizable. This result is not related to the well-known Craig interpolation theorem, although both results are named after the same mathematician, William Craig. == Recursive axiomatization == Let $A\_1,A\_2,\backslash dots$ be an enumeration of the axioms of a recursively enumerable set T of first-order formulas. Construct another set T * consisting of :$\backslash underbrace\_i$ for each positive integer ''i''. The deductive closures of T * and T are thus equivalent; the proof will show that T * is a decidable set. A decision procedure for T * lends itself according to the following informal reasoning. Each member of T * is either $A\_1$ or of the form :$\backslash underbrace\_j.$ Since each formula has finite length, it is checkable whether or not it is $A\_1$ or of the said form. If it is of the said form and consists of ''j'' conjuncts, it is in T * if it is the expression $A\_j$; otherwise it is not in T *. Again, it is checkable whether it is in fact $A\_n$ by going through the enumeration of the axioms of T and then checking symbol-for-symbol whether the expressions are identical. 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「Craig's theorem」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.