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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 Atomic model (mathematical logic) ： ウィキペディア英語版 Atomic model (mathematical logic) In model theory, an atomic model is a model such that the complete type of every tuple is axiomatized by a single formula. Such types are called principal types, and the formulas that axiomatize them are called complete formulas. ==Definitions== A complete type ''p''(''x''1, ..., ''x''''n'') is called principal (or atomic) if it is axiomatized by a single formula φ(''x''1, ..., ''x''''n'') ∈ ''p''(''x''1, ..., ''x''''n''). A formula φ in a complete theory ''T'' is called complete if for every other formula ψ(''x''1, ..., ''x''''n''), the formula φ implies exactly one of ψ and ¬ψ in ''T''.〔Some authors refer to complete formulas as "atomic formulas", but this is inconsistent with the purely syntactical notion of an atom or atomic formula as a formula that does not contain a proper subformula.〕 It follows that a complete type is principal if and only if it contains a complete formula. A model ''M'' of the theory is called atomic if every ''n''-tuple of elements of ''M'' satisfies a complete formula. 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「Atomic model (mathematical logic)」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.