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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 Łoś–Tarski preservation theorem ： ウィキペディア英語版 Łoś–Tarski preservation theorem The Łoś–Tarski theorem is a theorem in model theory, a branch of mathematics, that states that the set of formulas preserved under taking substructures is exactly the set of ''universal'' formulas (Hodges 1997). == Statement == Let $T$ be a theory in a first-order language $L$ and $\backslash Phi(\backslash bar)$ a set of formulas of $L$. (The set of sequence of variables $\backslash bar$ need not be finite.) Then the following are equivalent: # If $A$ and $B$ are models of $T$, $A\; \backslash subseteq\; B$, $\backslash bar$ is a sequence of elements of $A$ and $B\; \backslash models\; \backslash bigwedge\; \backslash Phi(\backslash bar)$, then $A\; \backslash models\; \backslash bigwedge\; \backslash Phi(\backslash bar)$. ($\backslash Phi$ is preserved in substructures for models of $T$) # $\backslash Phi$ is equivalent modulo $T$ to a set $\backslash Psi(\backslash bar)$ of $\backslash forall\_1$ formulas of $L$. A formula is $\backslash forall\_1$ if and only if it is of the form $\backslash forall\; \backslash bar\; ()$ where $\backslash psi(\backslash bar)$ is quantifier-free. Note that this property fails for finite models. 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「Łoś–Tarski preservation 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.