caa a22 4500 465779425 CHVBK 20180323111951.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF00370158 doi (NATIONALLICENCE)springer-10.1007/BF00370158 Kracht Marcus II. Mathematisches Institut, Arnimallee 3, 1000, Berlin 33, Germany aut An almost general splitting theorem for modal logic [Elektronische Daten] [Marcus Kracht] Given a normal (multi-)modal logic Θ a characterization is given of the finitely presentable algebras A whose logics L A split the lattice of normal extensions of Θ. This is a substantial generalization of Rautenberg [10] and [11] in which Θ 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 A L A 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 Λ splits the lattice of extensions of Θ then Λ is the logic of an algebra finitely presentable over Θ; in this respect our result remains partial. Polish Academy of Sciences, 1990 Studia Logica Kluwer Academic Publishers 49/4(1990-12-01), 455-470 0039-3215 49:4<455 1990 49 11225 https://doi.org/10.1007/BF00370158 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00370158 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kracht Marcus II. Mathematisches Institut, Arnimallee 3, 1000, Berlin 33, Germany aut NATIONALLICENCE 773 0- Studia Logica Kluwer Academic Publishers 49/4(1990-12-01), 455-470 0039-3215 49:4<455 1990 49 11225 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer