An almost general splitting theorem for modal logic |
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Authors: | Marcus Kracht |
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Affiliation: | (1) II. Mathematisches Institut, Arnimallee 3, 1000 Berlin 33, Germany |
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Abstract: | Given a normal (multi-)modal logic a characterization is given of the finitely presentable algebras A whose logics LA split the lattice of normal extensions of . This is a substantial generalization of Rautenberg [10] and [11] in which is assumed to be weakly transitive and A to be finite. We also obtain as a direct consequence a result by Blok [2] that for all cycle-free and finite ALA splits the lattice of normal extensions of K. Although we firmly believe it to be true, we have not been able to prove that if a logic splits the lattice of extensions of then is the logic of an algebra finitely presentable over ; in this respect our result remains partial. |
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