Answer by Elliot Glazer for Is this set theory equivalent to ZFC?
Accepting the convention that it is a logical axiom that the universe is nonempty, the answer is yes. We will formalize the transitive closure axiom schema (TC) as follows: for any definable (with...
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Consider a variant of set theory with these axioms:Extensionality,Regularity (foundation),Separation,Powerset,Axiom of Choice, andTransitive closure of a set-like relation is set-like.Update:This did...
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