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Xavier Caicedo

Xavier Caicedo Ferrer, Colombian mathematical logician (Cali, Valle del Cauca Department 03 December 1944 –

Regarded as a world expert on the utilization of topological structures as models for obtaining logic theorems


Showed that any operation defined implicity by a system of quasi-identities in the variety of divisible relatively pseudo-complemented MV algebras is given by a term of variety

With J. Iovino developed a maximality theorem that characterizes a class of [0,1](0,1]-valued logics in terms of a model-theoretic property (2014)

With G. Metcalfe, R.O. Rodríguez & J. Rogger. A finite model property for Godel modal logics. Lecture Notes Comp. Science 8071:226-37, 2013 

With F. Dechesne & T.M.V. Janssen presented a prenex form theorem for a version of Independence Friendly Logic (2009)

With R. Cignoli showed that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives are strongly complete with respect to valuation in Heyting algebras with additional operations (2001)

Enunciated the Caicedo-Krynicki prenex form theorem (1999)

Exposed the principles of a logic of extended and variable structures utilizing sheaves over topological spaces as natural models (1995)

Showed how Hilbert’s ε-symbol increases the expressive power of generalized quantifiers (1995)

Proposed a general notion of intuitionistic sentential connective in the semantical context of Kripke models (1995)

Generalized a theorem of Mundici relating compactness of a regular logic L to a strong form of normality of the associated spaces of models (1991)

Introduced a natural class of Th quantifiers which includes not only all monadic types but also all linear order quantifiers (1990)

With A.M. Sette showed how the formulae of a logic are invariants under the action of given pseudogroups of partial isomorfisms (1988)

Gave a simple solution to Friedman’s fourth problem (1986)

Showed that “every algebra in an equationally defined class of algebras K is a subdirect product of subdirectly irreducible algebras of K” (Birkhoff theorem) is true for any class of structures (1981)

Showed that monadic filter (cofilter) quantifiers are essentially the cardinal quantifiers (1981)

Gave a characterization by partial isomorfisms of elementary equivalence in logics generated by arbitrary families of quantifiers (1980)

A formal system for the non-theorems of the propositional calculus. Notre Dame J. Formal Logic 19:147-51, 1978