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Syntactic characterizations of classes of first-order structures in mathematical fuzzy logic

AuthorsBadia, Guillermo; Costa, Vicent ORCID ; Dellunde, Pilar CSIC ORCID ; Noguera, Carles CSIC ORCID
KeywordsGraded model theory
Mathematical fuzzy logic
Universal classes
Universal-existential classes
Amalgamation theorems
Preservation theorems
Issue Date22-Feb-2019
PublisherSpringer Nature
CitationSoft Computing 23(7): 2177–2186 (2019)
AbstractThis paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal–existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Loś–Tarski and the Chang–Loś–Suszko preservation theorems follow.
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