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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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Is the notion of measurable cardinal definable from the perspective of set-theoretical poten...

Yes, it is sufficient. Your question actually touches on a known, similar issue. A proper class is not an object in ZF, so in ZF we can't directly refer to it. Hence, again under the assumption we wor …
Wojciech Aleksander Wołoszyn's user avatar