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Answer by Asaf Karagila for Definability and the Separation and Replacement...
Henning answered the original question fairly well. Let me address the clarification.The proof that Replacement implies Separation can be really just put into reverse gear here. If Separation wasn't a...
View ArticleAnswer by hmakholm left over Monica for Definability and the Separation and...
Suppose you want to form $\{z\in X\mid \varphi(z,\vec w,X)\}$, without using Separation.Either there exists $z$ such that $z\in X\land \varphi(z,\vec w,X)$ or there doesn't. In the latter case, the set...
View ArticleDefinability and the Separation and Replacement Axiom Schemata
I am beginning to study Set Theory, so naturally one might begin with the axioms. When reading the schemata of separation and replacement, my initial thought was, "Why would we need separation if we...
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