Undefinability of propositional quantifiers in the modal system S4
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We show that (contrary to the parallel case of intuitionistic logic, see , ) there does not exist a translation fromS42 (the propositional modal systemS4 enriched with propositional quantifiers) intoS4 that preserves provability and reduces to identity for Boolean connectives and □.
1980 Mathematics subject classificationsPrimary 03B45, 06E25 Secondary 18C10
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