English

A dichotomy for some elementarily generated modal logics

Logic 2015-03-02 v2

Abstract

In this paper we consider the normal modal logics of elementary classes defined by first-order formulas of the form x0x1xnxiRλxj\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.

Keywords

Cite

@article{arxiv.1406.5700,
  title  = {A dichotomy for some elementarily generated modal logics},
  author = {Stanislav Kikot},
  journal= {arXiv preprint arXiv:1406.5700},
  year   = {2015}
}
R2 v1 2026-06-22T04:44:13.703Z