I was wondering if every set can be "transitized" - that is, made into a transitive version of itself. Is this basically what the Mostowski collapse says?
2026-04-03 11:50:31.1775217031
Transitive sets and the Mostowski collapse
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That is not the Mostowski collapse. The collapse says a partially ordered set with certain properties is isomorphic to a transitive set with the $\in$ as the order.
You seem to ask about transitive closure, which is the smallest transitive set which includes a particular set.