Large Cardinals
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JOHN_BASH
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MATHEMATICS
Set Theory
Large Cardinals
Exploring the vast infinities of large cardinals reveals the limits of standard set theory
19 Jan 2026
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Why are large cardinal axioms considered extensions beyond the standard ZFC axioms in set theory?
Because they contradict the axioms of ZFC and replace them entirely
Because their existence cannot be proven within ZFC and they strengthen the theory by assuming larger infinities
Because they are smaller infinite cardinals that simplify the ZFC axioms
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