Taming the 'Elsewhere': On Expressivity of Topological Languages

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F24%3A00558050" target="_blank" >RIV/67985807:_____/24:00558050 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1017/S1755020322000120" target="_blank" >http://dx.doi.org/10.1017/S1755020322000120</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S1755020322000120" target="_blank" >10.1017/S1755020322000120</a>

Result language
angličtina
Original language name
Taming the 'Elsewhere': On Expressivity of Topological Languages
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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