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A type of axioms of set theory stating a certain kind of “large” infinite cardinal(s) exists. This “large” is not in a sense that n+1 is larger than n, rather like that YHWH being transcendence of us. All known examples are “for now not inconsistent” with ZF(C), and climbing up higher in the hierarchy of large cardinals means gaining more consistency strength in the proper way. Well-knowns are: inaccessible, weekly compact, 0#, measurable, supercompact, and so on.
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