Source: J. Symbolic Logic
Volume 77, Issue 3
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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