Large Cardinals and...
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JOHN_BASH
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MATHEMATICS
Set Theory
Large Cardinals and Consistency
Exploring the profound impact of large cardinals on the foundations of mathematics and consistency
17 Jan 2026
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Why can't the existence of large cardinals be proven within the standard ZFC axioms?
Because large cardinal axioms extend beyond the strength of ZFC and introduce assumptions that cannot be derived from ZFC alone.
Because large cardinals are contradictory and thus cannot exist in any consistent system.
Because ZFC explicitly denies the existence of any infinite cardinals larger than aleph-null.
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