Models, Algebras and Proofs: Proceedings Latin-American Symposium on Mathematical Logic,1996, Bogota, Colombia

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"Contains a balanced account of recent advances in set theory, model theory, algebraic logic, and proof theory, originally presented at the Tenth Latin American Symposium on Mathematical Logic held in Bogata, Columbia. Traces new interactions among logic, mathematics, and computer science. Features original research from over 30 well-known experts worldwide."

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Editorial Reviews

Presents recent advances in set theory, model theory, algebraic logic, and proof theory in a collection of 22 papers selected from the 1996 symposium. Six of the papers discuss generic and end extensions of models of set theory, and relations between combinatorics and choice principles. Five articles on topics of model theory not amenable to first order methods are also included. The six papers on algebraic logic deal with generalized ideas as algebraic counterparts to theories, the algebraic meaning of the interpolation theorem, the geometric aspects of Lukasiewicz logics, and the algebraic semantics of particular logics. There are four articles on the strengths of various proof systems, and another on new logical paradigms brought forth by advances in AI. No index. Annotation c. by Book News, Inc., Portland, Or.
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Table of Contents

Set theory - generic absoluteness and forcing axioms; partition of the reals and choice; analogues of the MacDowell-Specker theorem for set theory; strict genericity; weak versions of the axiom of choice for families of finite sets; heights of models of ZFC and the existence of end elementary extensions; model theory; on the (infinite) model theory of fixed point logics; stable Banach spaces and Banach space structures; induction, games, and linear orderings; query completeness, distinguishability, and rational machines. Algebraic logic - ideals in quasivarieties of algebras; amalgamation and interpolation in abstract algebraic logic; symmetric intuitionistic connectives; matrix semantics for annotated logics; twenty questions with many-valued answers; Monadic De Morgan algebras. Proof systems -inductive theorem proving in hierarchical conditional specifications; general combinatorial principles in second order bounded arithmetic; towards an information logic; standardizing the N systems of Gentzen; translations between logics.

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