A new version of an old modal incompleteness theorem

Details A new version of an old modal incompleteness theorem A new version of an old modal incompleteness theorem

2012-02-15

arxiv.org/abs/1202.3268v1

Bulletin of the Section of Logic 39:3-4, pp. 199-204, 2010

Mathematics

Logic

4 pages

Scientific paper

Thomason \cite{Thomason74} showed that a certain modal logic $\mathbf{L}\subset \mathbf{S4}$ is incomplete with respect to Kripke semantics. Later Gerson \cite{Gerson75} showed that $\mathbf{L}$ is also incomplete with respect to neighborhood semantics. In this paper we show that $\mathbf{L}$ is in fact incomplete with respect to any class of complete Boolean algebras with operators, i.e. that it is completely incomplete.

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