What is the upper part of the lattice of bimodal logics?

Studia Logica 53 (2):235 - 241 (1994)
We define an embedding from the lattice of extensions ofT into the lattice of extensions of the bimodal logic with two monomodal operators 1 and 2, whose 2-fragment isS5 and 1-fragment is the logic of a two-element chain. This embedding reflects the fmp, decidability, completenes and compactness. It follows that the lattice of extension of a bimodal logic can be rather complicated even if the monomodal fragments of the logic belong to the upper part of the lattice of monomodal logics.
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DOI 10.1007/BF01054711
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R. A. Bull (1966). That All Normal Extensions of S4.3 Have the Finite Model Property. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 12 (1):341-344.

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