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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 Trakhtenbrot's theorem ： ウィキペディア英語版 Trakhtenbrot's theorem In Logic, finite model theory, and Computability Theory, Trakhtenbrot's theorem (due to Boris Trakhtenbrot) states that the problem of validity in First-order logic (FO) on the class of all finite models is undecidable. In fact, the class of valid sentences over finite models is not recursively enumerable (though it is co-recursively enumerable). It is considered a very important result, since it implies that the completeness theorem (that is fundamental to FO) does not hold in the finite case. Also it seems counter intuitive that being valid over all structures is 'easier' than over just the finite ones. The Theorem was first published in 1950: "The Impossibility of an Algorithm for the Decidability Problem on Finite Classes". ==Mathematical Formulation== We follow the formulations as in 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「Trakhtenbrot'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.