Taming the 'Elsewhere': On Expressivity of Topological Languages

0558050 - ÚI 2025 GB eng J - Journal Article
Fernández-Duque, David
Taming the 'Elsewhere': On Expressivity of Topological Languages.
Review of Symbolic Logic. Online 28 March 2022 (2024). ISSN 1755-0203. E-ISSN 1755-0211
Institutional support: RVO:67985807
Keywords : modal logic * topological semantics * expressivity
OECD category: Pure mathematics
Impact factor: 0.6, year: 2022
Method of publishing: Limited access
http://dx.doi.org/10.1017/S1755020322000120

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.


Permanent Link: http://hdl.handle.net/11104/0331859