Equality-free saturated models

Saturated models are a powerful tool in model theory. The properties of universality and homogeneity of the saturated models of a theory are useful for proving facts about this theory. They are used in the proof of interpolation and preservation theorems and also as work-spaces. Sometimes we work with models which are saturated only for some sets of formulas, for example, recursively saturated models, in the study of models of arithmetic or atomic compact, in model theory of modules. In this article we introduce the notion of equality-free saturated model, that is, roughly speaking, a model which is saturated for the set of equality-free formulas. Our aim is to understand better the role that identity plays in classical model theory, in particular with regard to this process of saturation. Given an infinite cardinal κ, we say that a model is equality-free κsaturated if it satisfies all the 1-types over sets of parameters of power less than κ, with all the formulas in the type that are equality-free. We compare this notion with the usual notion of κ-saturated model. We prove the existence of infinite models A, which are L −-|A | +-saturated. Fro

Revisiting Ultraproducts in Fuzzy Predicate Logics

Abstract-In this paper we examine different possibilities of defining reduced products and ultraproducts in fuzzy predicate logics. We present analogues to the Łos Theorem for these notions and discuss the advantages and drawbacks of each definition introduced. Following the work in [9], we show that these constructions are adequate for working in a reduced semantics

Revisiting ultraproducts in fuzzy predicate logics

In this paper we examine different possibilities of defining reduced products and ultraproducts in fuzzy predicate logics. We present analogues to the Łoś theorem for these notions and discuss the advantages and drawbacks of each definition introduced

Advances on elementary equivalence in model theory of fuzzy logics

Dellunde and Garca-Cerda~na are supported by EdeTRI (TIN2012-39348-C02-01); Garca-Cerda~na is also supported by the Spanish MICINN project MTM 201125745 and the grant 2009SGR 1433 from the Generalitat de Catalunya;Noguera is supported by the project GA13-14654S of the Czech Science Foundation and by the FP7-PEOPLE-2009-IRSES project MaToMUVI (PIRSES-GA-2009-247584)Peer Reviewe

On elementary equivalence in fuzzy predicate logics

Our work is a contribution to the model theory of fuzzy predicate logics. In this paper we characterize elementary equivalence between models of fuzzy predicate logic using elementary mappings. Refining the method of diagrams we give a solution to an open problem of Hájek and Cintula (J Symb Log 71(3):863-880, 2006, Conjectures 1 and 2). We investigate also the properties of elementary extensions in witnessed and quasi-witnessed theories, generalizing some results of Section 7 of Hájek and Cintula (J Symb Log 71(3):863-880, 2006) and of Section 4 of Cerami and Esteva (Arch Math Log 50(5/6):625-641, 2011) to non-exhaustive model

Extending possibilistic logic over Gödel logic

In this paper we present several fuzzy logics trying to capture different notions of necessity (in the sense of possibility theory) for Gödel logic formulas. Based on different characterizations of necessity measures on fuzzy sets, a group of logics with Kripke style semantics is built over a restricted language, namely, a two-level language composed of non-modal and modal formulas, the latter, moreover, not allowing for nested applications of the modal operator N. Completeness and some computational complexity results are shown

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

This 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 Los--Tarski and the Chang--Los--Suszko preservation theorems follow