[FOM] SOL vs. ZFC
JoeShipman at aol.com
Mon Jun 3 18:18:56 EDT 2013
The set of validities in Second Order Logic with standard semantics is Pi^1_2 complete, so we can't give a complete axiomatization. My question has two parts:
1) is there any commonly used system of axioms for second order logic that includes sentences which ZFC does not prove are validities?
2) is there any sentence which ZFC proves is a validity of second order logic, but which is not a consequence of any commonly used system of axioms for second order logic other than the system "enumerate sentences with ZFC-proofs of their validity"?
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