On elementary equivalence in fuzzy predicate logics
type: Item
instance of: scholarly article
title: On elementary equivalence in fuzzy predicate logics
zbMATH Open document ID: 1295.03013
author: Francesc Esteva
author: Pilar Dellunde
published in: Archive for Mathematical Logic
publication date: 2013-02-15T00:00:00Z
full work available at URL: http://ddd.uab.cat/record/153512
review text: This paper is a contribution to the model theory of fuzzy logic, building upon some previous work by \textit{P. Hájek} and \textit{P. Cintula} [J. Symb. Log. 71, No. 3, 863--880 (2006; Zbl 1111.03030)] where the basics of a theory of elementary equivalence for fuzzy predicate logics were developed. In particular, Hájek and Cintula had proved that in core fuzzy logics, a theory \(T'\) is a conservative extension of a theory \(T\) iff every exhaustive model of \(T\) can be elementarily one-to-one mapped into some model of \(T'\), and conjectured that the result continues to hold when ``exhaustive model'' is replaced by ``arbitrary model''. In this paper, the authors provide a counterexample to this conjecture. Other notable results in this article include a characterisation of elementary equivalence between models of fuzzy predicate logics that uses elementary mappings, as well as an investigation of the properties of elementary extensions in witnessed and quasi-witnessed theories.
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 03C07
zbMATH DE Number: 6136597
zbMATH Keywords: mathematical logic
zbMATH Keywords: model theory
zbMATH Keywords: fuzzy predicate logics
zbMATH Keywords: elementary extensions
zbMATH Keywords: witnessed models
zbMATH Keywords: quasi-witnessed models
MaRDI profile type: Publication
OpenAlex ID: W1988776462
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DOI: 10.1007/S00153-012-0303-X
description: scientific article; zbMATH DE number 6136597