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End extension : ウィキペディア英語版
End extension
In model theory and set theory, which are disciplines within mathematics, a model \mathfrak=\langle B, F\rangle of some axiom system of set theory T\, in the language of set theory is an end extension of \mathfrak=\langle A, E\rangle , in symbols \mathfrak\subseteq_\text\mathfrak, if
* \mathfrak is a substructure of \mathfrak, and
* b\in A whenever a\in A and bFa\, hold, i.e., no new elements are added by \mathfrak to the elements of \mathfrak.
The following is an equivalent definition of end extension: \mathfrak is a substructure of \mathfrak, and \=\ for all a\in A.
For example, \langle B, \in\rangle is an end extension of \langle A, \in\rangle if A\, and B\, are transitive sets, and A\subseteq B.


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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