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In mathematical logic, the Mostowski collapse lemma is a statement in set theory named for Andrzej Mostowski. ==Statement== Suppose that ''R'' is a binary relation on a class ''X'' such that *''R'' is set-like: ''R''−1() = is a set for every ''x'', *''R'' is well-founded: every nonempty subset ''S'' of ''X'' contains an ''R''-minimal element (i.e. an element ''x'' ∈ ''S'' such that ''R''−1() ∩ ''S'' is empty), *''R'' is extensional: ''R''−1() ≠ ''R''−1() for every distinct elements ''x'' and ''y'' of ''X'' The Mostowski collapse lemma states that for any such ''R'' there exists a unique transitive class (possibly proper) whose structure under the membership relation is isomorphic to (''X'', ''R''), and the isomorphism is unique. The isomorphism maps each element ''x'' of ''X'' to the set of images of elements ''y'' of ''X'' such that ''y R x'' (Jech 2003:69). 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「Mostowski collapse lemma」の詳細全文を読む スポンサード リンク
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