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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 Robinson's joint consistency theorem ： ウィキペディア英語版 Robinson's joint consistency theorem Robinson's joint consistency theorem is an important theorem of mathematical logic. It is related to Craig interpolation and Beth definability. The classical formulation of Robinson's joint consistency theorem is as follows: Let $T\_1$ and $T\_2$ be first-order theories. If $T\_1$ and $T\_2$ are consistent and the intersection $T\_1\backslash cap\; T\_2$ is complete (in the common language of $T\_1$ and $T\_2$), then the union $T\_1\backslash cup\; T\_2$ is consistent. Note that a theory is complete if it decides every formula, i.e. either $T\; \backslash vdash\; \backslash varphi$ or $T\; \backslash vdash\; \backslash neg\backslash varphi$. Since the completeness assumption is quite hard to fulfill, there is a variant of the theorem: Let $T\_1$ and $T\_2$ be first-order theories. If $T\_1$ and $T\_2$ are consistent and if there is no formula $\backslash varphi$ in the common language of $T\_1$ and $T\_2$ such that $T\_1\; \backslash vdash\; \backslash varphi$ and $T\_2\; \backslash vdash\; \backslash neg\backslash varphi$, then the union $T\_1\backslash cup\; T\_2$ is consistent. ==References== * 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「Robinson's joint consistency 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.