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Finite bases with respect to admissibility for modal logics of width 2. (English. Russian original) Zbl 0930.03020
Algebra Logika 38, No. 4, 436-455 (1999); translation in Algebra Logic 38, No. 4, 237-247 (1999).
Summary: It is proven that every finitely approximable and residually finite modal logic of depth 2 over K4 has a finite basis of admissible inference rules. This, in particular, implies that every finitely approximable residually finite modal logic of depth at most 2 is finitely based with respect to admissibility. (Among the logics of a larger depth or width, there are logics which do not have a finite, or even independent, basis of admissible rules of inference).

MSC:
03B45 Modal logic (including the logic of norms)
03G25 Other algebras related to logic
08C15 Quasivarieties
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