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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 Prime model ： ウィキペディア英語版 Prime model In mathematics, and in particular model theory, a prime model is a model which is as simple as possible. Specifically, a model $P$ is prime if it admits an elementary embedding into any model $M$ to which it is elementarily equivalent (that is, into any model $M$ satisfying the same complete theory as $P$). == Cardinality == In contrast with the notion of saturated model, prime models are restricted to very specific cardinalities by the Löwenheim-Skolem theorem. If $L$ is a first-order language with cardinality $\backslash kappa$ and $T$ a complete theory over $L,$ then this theorem guarantees a model for $T$ of cardinality $\backslash max(\backslash kappa,\backslash aleph\_0);$ therefore no prime model of $T$ can have larger cardinality since at the very least it must be elementarily embedded in such a model. This still leaves much ambiguity in the actual cardinality. In the case of countable languages, all prime models are at most countable. 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「Prime model」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.