Mathematical Logic Quarterly 50 (3):295-296 (2004)

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
Keywords Kripke model  well‐founded relation  Grzegorczyk's logic  axiom of choice
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DOI 10.1002/malq.200310094
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