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arXiv · 2109.06040

Taming the `elsewhere': On expressivity of topological languages

David Fernández-Duque
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Abstract

In topological modal logic, it is well known that the Cantor derivative is more expressive than the topological closure, and the `elsewhere,' or `difference,' operator is more expressive than the `somewhere' operator. In 2014, Kudinov and Shehtman asked whether the combination of closure and elsewhere becomes strictly more expressive when adding the Cantor derivative. In this paper we give an affirmative answer: in fact, the Cantor derivative alone can define properties of topological spaces not expressible with closure and elsewhere. To prove this, we develop a novel theory of morphisms which preserve formulas with the elsewhere operator.

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David Fernández-Duque. 2021-09-13. Taming the `elsewhere': On expressivity of topological languages. https://arxiv.org/abs/2109.06040

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