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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation

[axiom that new sets must be separated from old ones]

3 ideas
Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD]
The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy]
Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano]