This volume is a collection of papers on model theory and its applications. The longest paper, "Model Theory of Unitriangular Groups" by O. V. Belegradek, forms a subtle general theory behind Mal'tsev's famous correspondence between rings and groups. This is the first published paper on the topic. Given the present model-theoretic interest in algebraic groups, Belegradek's work is of particular interest to logicians and algebraists.

The rest of the collection consists of papers on various questions of model theory, mainly on stability theory. Contributors are leading Russian researchers in the field.

Readership

Graduate students and research mathematicians interested in logic and foundations.

Table of Contents

• O. V. Belegradek -- Model theory of unitriangular groups
• O. V. Belegradek -- Model theory of locally free algebras
• A. A. Voronkov -- Model theory based on the notion of truth in the constructive sense
• B. I. Zil'ber -- Hereditarily transitive groups and quasi-Urbanik structures
• K. Zh. Kudaibergenov -- The number of homogeneous models of a complete theory
• T. G. Mustafin -- The stability theory of polygons
• E. A. Palyutin and S. S. Starchenko -- Horn theories with nonmaximal spectrum
• A. N. Ryaskin -- The number of models of complete theories of unars
• M. G. Peretyat'kin -- Finitely axiomatizable theories and similarity relations