Abstract

Grzegorczyk's modal logic corresponds to the class of upwards well-founded partially ordered Kripke frames, however all known proofs of this fact utilize some form of the Axiom of Choice; G. Boolos asked in [1], whether it is provable in plain ZF. We answer his question negatively: Grz corresponds to a class of frames, which does not provably coincide with upwards well-founded posets in ZF alone