Definition:ZFC/Historical Note

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Historical Note on ZFC

ZFC is generally accepted by mathematicians as a "reasonably good foundation" of mathematics.

We are far from claiming superiority of ZFC over alternative foundations of mathematics. For whatever reason, it won the competition. It does a decent job; so let us stick to it. It should be pointed out though that, to the best of our knowledge, none of the competitors to ZFC resolves the question of truth or falsity of CH, SH, MA, $\diamondsuit$, or of any other statement whose independence of ZFC has been established by the method of forcing.
-- 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics: Introduction