Conversion of Set Theory Problems to other fields

AI Thread Summary
The discussion explores the possibility of proving the consistency and independence of axioms by translating set theory problems into other fields, such as algebra. It highlights that one does not necessarily need to shift to other fields, as certain axioms, like ZFC combined with large cardinal axioms, can sufficiently demonstrate the consistency of ZFC. Participants express interest in further investigating these connections. The conversation emphasizes the interplay between different mathematical domains in addressing foundational questions. Overall, the topic underscores the potential for cross-disciplinary approaches in mathematical logic.
phoenixthoth
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Is there a way to prove axioms are consistent and/or independent by converting the problem of consistency/independence to another field, such as algebra?
 
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Sure.

You don't even have to go to other fields -- e.g. ZFC + any large cardinal axiom is strong enough to prove ZFC consistent.
 
Thanks, I'll look into that. :biggrin:
 
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