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 Sent from my iPhone