Non-finitely axiomatisable two-dimensional modal logics
Agi Kurucz and Sérgio Marcelino
Source: J. Symbolic Logic Volume 77, Issue 3
(2012), 970-986.
Abstract
We show the first examples of recursively enumerable (even decidable) two-dimensional products of finitely axiomatisable modal logics that are not finitely axiomatisable. In particular, we show that any axiomatisation of some bimodal logics that are determined by classes of product frames with linearly ordered first components must be infinite in two senses: It should contain infinitely many propositional variables, and formulas of arbitrarily large modal nesting-depth.
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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1344862170
Zentralblatt MATH identifier: 06083961
Digital Object Identifier: doi:10.2178/jsl/1344862170
Mathematical Reviews number (MathSciNet): MR2987146
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