DEFINABILITY IN NORMAL EXTENSIONS OF S4

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Abstract

A projective Beth property, PB2, in normal modal logics extending S4 is studied. A convenient criterion is furnished for PB2 to be valid in a larger family of extensions of K4. All locally tabular extensions of the Grzegorczyk logic with PB2 are described. Superintuitionistic logics with the projective Beth property that have no modal companions with this property are found.

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