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forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.

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An exercise in Kunen. Getting Axiom of Replacement from set-like transitive closure.

I am studying Kunen's Set Theory (2011 edition) on my own. I got stuck at the excercise I.9.6 which is: Excercise I.9.6. Derive the axiom of replacement from lemma I.9.5. And the mentioned lemma is …
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