{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T12:07:27Z","timestamp":1759147647410,"version":"3.37.3"},"reference-count":36,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2020,8,3]],"date-time":"2020-08-03T00:00:00Z","timestamp":1596412800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001824","name":"Czech Science Foundation","doi-asserted-by":"publisher","award":["GA17-04630S"],"award-info":[{"award-number":["GA17-04630S"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,1,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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 $\\kappa $-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\u2013Vaught theorem on unions of elementary chains. Finally, we provide a structural characterization of $\\kappa $-saturation in terms of the completion of a diagram representing a certain configuration of models and mappings.<\/jats:p>","DOI":"10.1093\/jigpal\/jzaa027","type":"journal-article","created":{"date-parts":[[2020,6,25]],"date-time":"2020-06-25T03:37:26Z","timestamp":1593056246000},"page":"1-20","source":"Crossref","is-referenced-by-count":1,"title":["Saturated models of first-order many-valued logics"],"prefix":"10.1093","volume":"30","author":[{"given":"Guillermo","family":"Badia","sequence":"first","affiliation":[{"name":"School of Historical and Philosophical Inquiry, University of Queensland, Brisbane, St Lucia, QLD 4072, Australia"}]},{"given":"Carles","family":"Noguera","sequence":"additional","affiliation":[{"name":"Institute of Information Theory and Automation, Czech Academy of Sciences, Pod vod\u00e1renskou v\u011b\u017e\u00ed 4, 182 00 Prague, Czech Republic"}]}],"member":"286","published-online":{"date-parts":[[2020,8,3]]},"reference":[{"key":"2022011721250344300_ref1","doi-asserted-by":"crossref","first-page":"2177","DOI":"10.1007\/s00500-019-03850-6","article-title":"Syntactic characterizations of classes of first-order structures in mathematical fuzzy logic","volume":"23","author":"Badia","year":"2019","journal-title":"Soft Computing"},{"key":"2022011721250344300_ref2","first-page":"150","article-title":"Saturated models in mathematical fuzzy logic","volume-title":"Proceedings of the IEEE International Symposium on Multiple-Valued Logic","author":"Badia","year":"2018"},{"key":"2022011721250344300_ref3","article-title":"A general omitting types theorem in mathematical fuzzy logic","author":"Badia","year":"2020","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"2022011721250344300_ref4","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.tcs.2018.05.010","article-title":"Fra\u00efss\u00e9 classes of graded relational structures","volume":"737","author":"Badia","year":"2018","journal-title":"Theoretical Computer Science"},{"key":"2022011721250344300_ref5","article-title":"Model theory for metric structures","volume-title":"Model Theory with Applications to Algebra and Analysis, vol. 2, Volume 350 of London Mathematical Society Lecture Note Series, Z. 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