The McKinsey--Lemmon Logic Is Barely Canonical
Robert Goldblatt and Ian Hodkinson
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.