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  1. Xavier Caicedo (2015). Lindström’s Theorem for Positive Logics, a Topological View. [REVIEW] In Andrés Villaveces, Roman Kossak, Juha Kontinen & Åsa Hirvonen (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter. 73-90.
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  2. Xavier Caicedo & José Iovino (2014). Omitting Uncountable Types and the Strength of [0,1]-Valued Logics. 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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  3. Xavier Caicedo & Ricardo O. Rodriguez (2010). Standard Gödel Modal Logics. Studia Logica 94 (2):189 - 214.
    We prove strong completeness of the □-version and the ◊-version of a Gödel modal logic based on Kripke models where propositions at each world and the accessibility relation are both infinitely valued in the standard Gödel algebra [0,1]. Some asymmetries are revealed: validity in the first logic is reducible to the class of frames having two-valued accessibility relation and this logic does not enjoy the finite model property, while validity in the second logic requires truly fuzzy accessibility relations and this (...)
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  4. Xavier Caicedo, Francien Dechesne & Theo Janssen (2009). Equivalence and Quantifier Rules for Logic with Imperfect Information. Logic Journal of the Igpl 17 (1):91-129.
    In this paper, we present a prenex form theorem for a version of Independence Friendly logic, a logic with imperfect information. Lifting classical results to such logics turns out not to be straightforward, because independence conditions make the formulas sensitive to signalling phenomena. In particular, nested quantification over the same variable is shown to cause problems. For instance, renaming of bound variables may change the interpretations of a formula, there are only restricted quantifier extraction theorems, and slashed connectives cannot be (...)
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  5. Graham Priest & Xavier Caicedo (2007). International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science. Synthese 158 (1):153-163.
  6. Xavier Caicedo (2004). Definability and Automorphisms in Abstract Logics. Archive for Mathematical Logic 43 (8):937-945.
    In any model theoretic logic, Beth’s definability property together with Feferman-Vaught’s uniform reduction property for pairs imply recursive compactness, and the existence of models with infinitely many automorphisms for sentences having infinite models. The stronger Craig’s interpolation property plus the uniform reduction property for pairs yield a recursive version of Ehrenfeucht-Mostowski’s theorem. Adding compactness, we obtain the full version of this theorem. Various combinations of definability and uniform reduction relative to other logics yield corresponding results on the existence of non-rigid (...)
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  7. Xavier Caicedo (2004). Implicit Connectives of Algebraizable Logics. Studia Logica 78 (1-2):155 - 170.
    An extensions by new axioms and rules of an algebraizable logic in the sense of Blok and Pigozzi is not necessarily algebraizable if it involves new connective symbols, or it may be algebraizable in an essentially different way than the original logic. However, extension whose axioms and rules define implicitly the new connectives are algebraizable, via the same equivalence formulas and defining equations of the original logic, by enriched algebras of its equivalente quasivariety semantics. For certain strongly algebraizable logics, all (...)
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  8. Xavier Caicedo & Roberto Cignoli (2001). An Algebraic Approach to Intuitionistic Connectives. Journal of Symbolic Logic 66 (4):1620-1636.
    It is shown that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives, including those proposed by Gabbay, are strongly complete with respect to valuations in Heyting algebras with additional operations. In all cases, the double negation of such a connective is equivalent to a formula of intuitionistic calculus. Thus, under the excluded third law it collapses to a classical formula, showing that this condition in Gabbay's definition is redundant. Moreover, such connectives can not be interpreted in all Heyting (...)
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  9. Xavier Caicedo & Alejandro Martín (2001). Completud de Dos Cálculos Logicos de Leibniz (Completencss of Two Logical Systems of Leibniz). Theoria 16 (3):539-558.
    Este trabajo se encuadra dentro de una nueva visión de la lógica de Leibniz, la cual pretende mostrar que sus escritos fueron ricos no solamente en proyectos ambiciosos (Característica Universal, Combinatoria, Mathesis) sino también en desarrollos lógico-matematicos concretos. Se demuestra que su “Caracteristica Numerica” que asigna pares de números a las proposiciones categóricas es una semántiea para la cual la silogística aristotélica es correcta y completa, y que el sistema algebraico presentado en Fundamentos de un Cálculo Lógico es una lógica (...)
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  10. Xavier Caicedo & Carlos H. Montenegro (1999). Models, Algebras, and Proofs Selected Papers of the X Latin American Symposium on Mathematical Logic Held in Bogotá.
     
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  11. Xavier Caicedo (1996). X Latin American Symposium on Mathematical Logic. Association for Symbolic Logic: The Bulletin of Symbolic Logic 2 (2):214-237.
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  12. Xavier Caicedo (1995). Continuous Operations on Spaces of Structures. In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers. 263--296.
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  13. Xavier Caicedo (1995). Hilbert's Ε-Symbol in the Presence of Generalized Quantifiers. In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers. 63--78.
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  14. Xavier Caicedo (1993). Compactness and Normality in Abstract Logics. Annals of Pure and Applied Logic 59 (1):33-43.
    We generalize a theorem of Mundici relating compactness of a regular logic L to a strong form of normality of the associated spaces of models. Moreover, it is shown that compactness is in fact equivalent to ordinary normality of the model spaces when L has uniform reduction for infinite disjoint sums of structures. Some applications follow. For example, a countably generated logic is countably compact if and only if every clopen class in the model spaces is elementary. The model spaces (...)
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  15. Xavier Caicedo (1991). Hilbert∈-Symbol in the Presence of Generalized Quantifiers. Bulletin of the Section of Logic 20 (3/4):85-86.
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  16. Xavier Caicedo (1990). Definability Properties and the Congruence Closure. Archive for Mathematical Logic 30 (4):231-240.
    We introduce a natural class of quantifiersTh containing all monadic type quantifiers, all quantifiers for linear orders, quantifiers for isomorphism, Ramsey type quantifiers, and plenty more, showing that no sublogic ofL ωω (Th) or countably compact regular sublogic ofL ∞ω (Th), properly extendingL ωω , satisfies the uniform reduction property for quotients. As a consequence, none of these logics satisfies eitherΔ-interpolation or Beth's definability theorem when closed under relativizations. We also show the failure of both properties for any sublogic ofL (...)
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  17. Xavier Caicedo (1986). A Simple Solution to Friedman's Fourth Problem. Journal of Symbolic Logic 51 (3):778-784.
    It is shown that Friedman's problem, whether there exists a proper extension of first order logic satisfying the compactness and interpolation theorems, has extremely simple positive solutions if one considers extensions by generalized (finitary) propositional connectives. This does not solve, however, the problem of whether such extensions exist which are also closed under relativization of formulas.
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  18. Xavier Caicedo, Rolando Chauqui, Newton C. D. Costa & Carlos A. di Prisco (1984). Meeting of the Assocaition for Symbolic Logic: Caracas, Venezuela, 1983. Journal of Symbolic Logic 49 (4):1430-1440.
  19. Xavier Caicedo, Rolando Chauqui, Newton C. D. da Costa & Carlos A. di Prisco (1984). Meeting of the Assocaition for Symbolic Logic: Caracas, Venezuela, 1983. Journal of Symbolic Logic 49 (4):1430-1440.
  20. Xavier Caicedo, Rolando Chauqui, Newton C. D. da Costa & Carlos A. Di Prisco (1984). Meeting of the Assocaition for Symbolic Logic: Caracas, Venezuela, 1983. Journal of Symbolic Logic 49 (4):1430 - 1440.
  21. Ayda I. Arruda, Xavier Caicedo, Rolando Chuaqui & Newton C. A. Costa (1983). Meeting of the Association for Symbolic Logic: Bogotá, Colombia, 1981. Journal of Symbolic Logic 48 (3):884-892.
  22. Ayda I. Arruda, Xavier Caicedo, Rolando Chuaqui & Newton C. A. da Costa (1983). Meeting of the Association for Symbolic Logic: Bogotá, Colombia, 1981. Journal of Symbolic Logic 48 (3):884 - 892.
  23. Xavier Caicedo (1981). On Extensions of $L{\Omega \Omega }(Q1)$. Notre Dame Journal of Formal Logic 22 (1):85-93.
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