I have read in a lot of set theory textbooks about large cardinals and large cardinal axioms. But what is the precise definition of a large cardinal axiom? Is there a rigorous definition of when an axiom $A$ that is not provable from $ZFC$ is a large cardinal axiom?
2026-03-30 14:10:45.1774879845
What is the rigorous definition of a large cardinal axiom?
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There is no accepted rigorous definition of "large cardinal axiom," although there are a couple rigorous notions one might consider plausible candidates. See the discussion here.