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In mathematical model theory, an imaginary element of a structure is roughly a definable equivalence class. These were introduced by , and elimination of imaginaries was introduced by ==Definitions== *''M'' is a model of some theory. *x and y stand for ''n''-tuples of variables, for some natural number ''n''. *An equivalence formula is a formula φ(x,y) that is a symmetric and transitive relation. Its domain is the set of elements a of ''M''''n'' such that φ(a,a); it is an equivalence relation on its domain. *An imaginary element a/φ of ''M'' is an equivalence formula φ together with an equivalence class a. *''M'' has elimination of imaginaries if for every imaginary element a/φ there is a formula θ(x,y) such that there is a unique tuple b so that the equivalence class of a consists of the tuples x such that θ(x,b) *A model has uniform elimination of imaginaries if the formula θ can be chosen independently of a. *A theory has elimination of imaginaries if every model does (and similarly for uniform elimination). 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「Imaginary element」の詳細全文を読む スポンサード リンク
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