Lindström theorems in graded model theory

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F21%3A00537229" target="_blank" >RIV/67985556:_____/21:00537229 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0168007220301408" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0168007220301408</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.apal.2020.102916" target="_blank" >10.1016/j.apal.2020.102916</a>

Result language
angličtina
Original language name
Lindström theorems in graded model theory
Original language description
Stemming from the works of Petr Hájek on mathematical fuzzy logic, graded model theory has been developed by several authors in the last two decades as an extension of classical model theory that studies the semantics of many-valued predicate logics. In this paper we take the first steps towards an abstract formulation of this model theory. We give a general notion of abstract logic based on many-valued models and prove six Lindström-style characterizations of maximality of first-order logics in terms of metalogical properties such as compactness, abstract completeness, the Löwenheim–Skolem property, the Tarski union property, and the Robinson property, among others. As necessary technical restrictions, we assume that the models are valued on finite MTL-chains and the language has a constant for each truth-value.
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
10102 - Applied mathematics

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

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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