The McKinsey–Lemmon logic is barely canonical

Australasian Journal of Logic 5:1-19 (2007)
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Abstract

We study a canonical modal logic introduced by Lemmon, and axiomatised by an infinite sequence of axioms generalising McKinsey’s formula. We prove that the class of all frames for this logic is not closed under elementary equivalence, and so is non-elementary. We also show that any axiomatisation of the logic involves infinitely many non-canonical formulas.

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References found in this work

[Omnibus Review].Robert Goldblatt - 1986 - Journal of Symbolic Logic 51 (1):225-227.
An introduction to modal logic: the Lemmon notes.E. J. Lemmon - 1977 - Oxford: Blackwell. Edited by Dana S. Scott.
Normal forms in modal logic.Kit Fine - 1975 - Notre Dame Journal of Formal Logic 16 (2):229-237.

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