A new version of an old modal incompleteness theorem

Jacob Vosmaer

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arXiv · 1202.3268

A new version of an old modal incompleteness theorem

Jacob Vosmaer

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Abstract

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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BibTeX RIS

Jacob Vosmaer. 2012-02-15. A new version of an old modal incompleteness theorem. https://arxiv.org/abs/1202.3268

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