Large cardinal axiom

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.

I proved at late last night the statement is actually consistent! What? Yeah, relative to a large cardinal axiom, of course.

俚语	large cardinal axiom
释义	Large cardinal axiom 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. I proved at late last night the statement is actually consistent! What? Yeah, relative to a large cardinal axiom, of course.
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