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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 Hrushovski construction ： ウィキペディア英語版 Hrushovski construction In model theory, a branch of mathematical logic, the Hrushovski construction generalizes the Fraïssé limit by working with a notion of ''strong substructure'' $\backslash leq$ rather than $\backslash subseteq$. It can be thought of as a kind of "model-theoretic forcing", where a (usually) stable structure is created, called the ''generic''. The specifics of $\backslash leq$ determine various properties of the generic, with its geometric properties being of particular interest. It was initially used by Ehud Hrushovski to generate a stable structure with an "exotic" geometry, thereby refuting Zil'ber's Conjecture. == Three conjectures == The initial applications of the Hrushovski construction refuted two conjectures and answered a third question in the negative. Specifically, we have: * Lachlan's Conjecture Any stable $\backslash aleph\_0$-categorical theory is totally transcendental. * Zil'ber's Conjecture Any uncountably categorical theory is either locally modular or interprets an algebraically closed field. * Cherlin's Question Is there a maximal (with respect to expansions) strongly minimal set? 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「Hrushovski construction」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.