Incomparable consistency strengths

JOSEPH SHIPMAN joeshipman at aol.com
Thu Apr 29 12:50:33 EDT 2021


Can anyone give explicitly (not merely prove they exist, but actually give the axioms or schemes in a level of specificity and detail typical of published math papers) two axiomatized theories A and B such that 
1) ZF proves Con(A)
2) ZF proves Con(B)
3) PA does not prove Con(A)->Con(B)
4) PA does not prove Con(B)->Con(A)
?

— JS

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