Applications of ultraproducts: From compactness to fuzzy elementary classes

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7 Citations (Scopus)

Abstract

In this article we present different applications of the ultraproduct construction in fuzzy predicate logics. Under the assumptions either of the existence of a measurable cardinal or that the MTL-algebra is finite, we show that basic properties of fuzzy structures are preserved under ultraproducts, we prove that ultraproducts of safe (exhaustive, witnessed) models are safe (exhaustive, witnessed, respectively). Finally, we show that, in the case of finite MTL-algebras, ultraproducts can be used to give an algebraic proof of the Compactness Theorem and a Characterization Theorem for Elementary Classes. © The Author 2013. Published by Oxford University Press. All rights reserved.
Original languageEnglish
Article numberjzt041
Pages (from-to)166-180
JournalLogic Journal of the IGPL
Volume22
Issue number1
DOIs
Publication statusPublished - 1 Feb 2014

Keywords

  • Fuzzy predicate logics
  • Model theory
  • Ultraproducts

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