Paper Info
Title
Saturated models of first-order many-valued logics
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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\kappa $</tex> -saturated model, i.e. a model where as many types as possible are realized. In order to prove this theorem we obtain, as by-products, some results on tableaux (understood as pairs of sets of formulas) and their consistency and satisfiability and a generalization of the Tarski–Vaught theorem on unions of elementary chains. Finally, we provide a structural characterization of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\kappa $</tex> -saturation in terms of the completion of a diagram representing a certain configuration of models and mappings.
Year
DOI
Venue
2022
10.1093/jigpal/jzaa027
Logic Journal of the IGPL
Keywords
DocType
Volume
Mathematical fuzzy logic,first-order graded logics,uninorms,residuated lattices,logic UL,types,saturated models,elementary chains
Journal
30
Issue
ISSN
Citations 
1
1367-0751
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
guillermo badia155.53
Carles Noguera200.34