Applications of ultraproducts: From compactness to fuzzy elementary classes

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.Research partially funded by the Spanish projects Agreement Technologies CONSOLIDER (CSD2007-0022), EdeTRI (TIN2012-39348-C02-01) and by the Generalitat de Catalunya under the grant 2009-SGR-1434Peer Reviewe