Abstract
In this paper we consider the normal modal logics of elementary classes defined by first-order formulas of the form \({\forall x_0 \exists x_1 \dots \exists x_n \bigwedge x_i R_\lambda x_j}\). We prove that many properties of these logics, such as finite axiomatisability, elementarity, axiomatisability by a set of canonical formulas or by a single generalised Sahlqvist formula, together with modal definability of the initial formula, either simultaneously hold or simultaneously do not hold.
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Kikot, S. A Dichotomy for Some Elementarily Generated Modal Logics. Stud Logica 103, 1063–1093 (2015). https://doi.org/10.1007/s11225-015-9611-6
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DOI: https://doi.org/10.1007/s11225-015-9611-6