0537231 20240103225102.320210111235959.9 000744508900001 85050989071 10.1093/jigpal/jzaa027 22 s. P cav_un_epca*02583581367-0751301 (2022)1-20Oxford University Press mathematical fuzzy logic first-order graded logics uninorms cav_un_auth*0382241 Badia G. AU 50 cav_un_auth*0293476 Noguera Carles UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory 50 A Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2021/MTR/noguera-0537231.pdf https://academic.oup.com/jigpal/article-abstract/30/1/1/5879257?redirectedFrom=fulltext GA17-04630S GA ČR cav_un_auth*0349495 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. WOS BA 10000 10100 10102 2022 2 RVO:67985556 http://hdl.handle.net/11104/0315000 1 S 3+4 Article Mathematics Applied|Mathematics|Logic C MATHEMATICS|MATHEMATICS.APPLIED|LOGIC 0.9 0.2 6.7 0.00087 0.349 615 0.411 0.900 93 Q1 61.2 Q4 Q2 0.9 Q1 88.1 2022 85050989071 SCOPUS PUBMED 000744508900001 WOS cav_un_epca*0258358 Logic Journal of the IGPL 1367-0751 1368-9894 Roč. 30 č. 1 2022 1 20 Oxford University Press