On Axiomatising Products of Kripke Frames, part II
Agi Kurucz · 2008
abstract. We generalise some results of [7, 5] and show that if L is an α-modal logic (for some ordinal α ≥ 3) such that (i) L contains the product logic Kα and (ii) the product of α-many trees of depth one and with arbitrary large finite branching is a frame for L, then any axiomatisation of L must contain infinitely many propositional variables. As a consequence we obtain that product logics like Kα, K4α, S4α, GLα, and Grzα cannot be axiomatised using finitely many propositional variables, whenever α ≥ 3.