Logic Journal of the IGPL 30 (1):1-20 (2022)

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Abstract
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 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 $\kappa $-saturation in terms of the completion of a diagram representing a certain configuration of models and mappings.
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DOI 10.1093/jigpal/jzaa027
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References found in this work BETA

[Introduction].Wilfrid Hodges - 1988 - Journal of Symbolic Logic 53 (1):1.
[Introduction].Wilfrid Hodges - 1986 - Journal of Symbolic Logic 51 (4):865.
Substructural Fuzzy Logics.George Metcalfe & Franco Montagna - 2007 - Journal of Symbolic Logic 72 (3):834 - 864.
On Theories and Models in Fuzzy Predicate Logics.Petr Hájek & Petr Cintula - 2006 - Journal of Symbolic Logic 71 (3):863 - 880.

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Citations of this work BETA

Lindström Theorems in Graded Model Theory.Guillermo Badia & Carles Noguera - 2021 - Annals of Pure and Applied Logic 172 (3):102916.

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