Mostowski Collapse

The Mostowski collapse lemma states that for any structure S with a well-founded relation R such that {y : y R x} is a set, and such that R satisfies extensionality, there exists a transitive class C (possibly proper) whose structure under the membership relation is isomorphic to S. The isomorphism maps each element x of S to the set of images of elements y of S such that y R x.

 

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