Institute of Information Theory and Automation

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Bibliography

Journal Article

Saturated models of first-order many-valued logics

Badia G., Noguera Carles

: Logic Journal of the IGPL vol.30, 1 (2022), p. 1-20

: GA17-04630S, GA ČR

: mathematical fuzzy logic, first-order graded logics, uninorms

: 10.1093/jigpal/jzaa027

: http://library.utia.cas.cz/separaty/2021/MTR/noguera-0537231.pdf

: https://academic.oup.com/jigpal/article-abstract/30/1/1/5879257?redirectedFrom=fulltext

(eng): This paper is devoted to the problem of existence of saturated models for first-order many-valued logics. We consider a general notion of type as pairs of sets of formulas in one free variable that express properties that an element of a model should, respectively, satisfy and falsify. By means of an elementary chains construction, we prove that each model can be elementarily extended to a κ-saturated model, i.e. a model where as many types as possible are realized. In order to prove this theorem we obtain, as by-products, some results on tableaux (understood as pairs of sets of formulas) and their consistency and satisfiability and a generalization of the Tarski-Vaught theorem on unions of elementary chains. Finally, we provide a structural characterization of κ-saturation in terms of the completion of a diagram representing a certain configuration of models and mappings.

: BA

: 10102

2019-01-07 08:39