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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DOI 10.26686/ajl.v5i0.1783
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References found in this work BETA

[Omnibus Review].Robert Goldblatt - 1986 - Journal of Symbolic Logic 51 (1):225-227.
Normal Forms in Modal Logic.Kit Fine - 1975 - Notre Dame Journal of Formal Logic 16 (2):229-237.

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Bare Canonicity of Representable Cylindric and Polyadic Algebras.Jannis Bulian & Ian Hodkinson - 2013 - Annals of Pure and Applied Logic 164 (9):884-906.
The Boxdot Conjecture and the Generalized McKinsey Axiom.Christopher Steinsvold - 2018 - Australasian Journal of Logic 15 (3):630-641.

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