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Continuous operations on spaces of structures

In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers. pp. 263--296 (1995)

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  1. Compactification of l(q).Antonio Mario Sette & José Carlos Cifuentes - 2000 - Synthese 125 (1-2):247 - 252.
    In this paper we extend the usual notion of model (asa structure) to the more general notion of CauchySequence of Structures in a similar way as rationalsare extending to real numbers by means of Cauchysequences of rationals. We show that the structurespace St is dense in thecomplete space CSt of Cauchysequences of structures and that CSt is compact in the (topo)logicalsense.
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  • Omitting uncountable types and the strength of [0,1]-valued logics.Xavier Caicedo & José N. Iovino - 2014 - Annals of Pure and Applied Logic 165 (6):1169-1200.
    We study a class of [0,1][0,1]-valued logics. The main result of the paper is a maximality theorem that characterizes these logics in terms of a model-theoretic property, namely, an extension of the omitting types theorem to uncountable languages.
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