Fixed point logics and definable topological properties
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F24%3A00580737" target="_blank" >RIV/67985807:_____/24:00580737 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1017/S0960129523000385" target="_blank" >https://doi.org/10.1017/S0960129523000385</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S0960129523000385" target="_blank" >10.1017/S0960129523000385</a>
Alternative languages
Result language
angličtina
Original language name
Fixed point logics and definable topological properties
Original language description
Modal logic enjoys topological semantics that may be traced back to McKinsey and Tarski, and the classification of topological spaces via modal axioms is a lively area of research. In the past two decades, there has been interest in extending topological modal logic to the language of the mu-calculus, but previously no class of topological spaces was known to be mu-calculus definable that was not already modally definable. In this paper, we show that the full mu-calculus is indeed more expressive than standard modal logic, in the sense that there are classes of topological spaces (and weakly transitive Kripke frames), which are mu-definable but not modally definable. The classes we exhibit satisfy a modally definable property outside of their perfect core, and thus we dub them imperfect spaces. We show that the mu-calculus is sound and complete for these classes. Our examples are minimal in the sense that they use a single instance of a greatest fixed point, and we show that least fixed points alone do not suffice to define any class of spaces that is not already modally definable.
Czech name
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Czech description
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Classification
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
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Structures in Computer Science
ISSN
0960-1295
e-ISSN
1469-8072
Volume of the periodical
34
Issue of the periodical within the volume
2
Country of publishing house
GB - UNITED KINGDOM
Number of pages
17
Pages from-to
81-97
UT code for WoS article
001124258200001
EID of the result in the Scopus database
2-s2.0-85179984864