The McKinsey–Lemmon logic is barely canonical
Robert Goldblatt, Ian Hodkinson · The Australasian Journal of Logic · 2007
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.