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Philosophical aspects of logic and set theory; truth status of mathematical axioms; Philosophy of Mathematics; philosophical aspects of mathematics in general; relation of mathematics to philosophy; etc. Consider also posting at http://philosophy.stackexchange.com/, where philosophy-of-mathematics is one of the most popular tags.

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The universe of sets, existential quantification in set theory

Yesterday, I posted a question that was received in a different way than I intended it. I would like to ask it again by adding some context. In ZF one can prove $\not\exists x (\forall y (y\in x)).$ …