Algebras of Distributions of Binary Isolating Formulas for Almost ω-Categorical Weakly o-Minimal Theories

Algebra and Logic - We describe distribution algebras of binary isolating formulas over 1-type for almost ω-categorical weakly o-minimal theories. It is proved that an isomorphism of these...     

Complete Theories with Finitely Many Countable Models. I

A syntactic characterization is furnished for the class of elementary complete theories with finitely many countable models, which is the analog of a known theorem by Ryll-Nardzewski on countably categorical theories, and is based on classifying the theories by Rudin-Keisler quasiorders and distribution functions of a number of models limit over types.     

Partial algebras associated with polygonometries of group pairs

We argue that there exists a relationship between pairs of groups and partial algebras. It is proved that connected polygonometries of group pairs are uniquely (up to isomorphism) determined by corresponding partial algebras. A class of all partial algebras associated with polygonometries of group pairs is shown to be axiomatizable. A class of partial algebras corresponding to trigonometries of group pairs on a projective plane is stated to be finitely axiomatizable. We also study the problem of being closed under the basic algebraic operations for the class of polygonometric algebras, and shed light on the interplay between homomorphism categories of connected polygonometries and polygonometric algebras. Supported by RFFR grant No. 93-01-01520 and by the AMS. Translated from Algebra i Logika, Vol. 36, No. 4, pp. 454–476, July–August, 1997.     

Hypergraphs of prime models and distributions of countable models of small theories

Hypergraphs of prime models over realizations of types in small theories are defined. On the basis of graph structures of models of small theories, hierarchies of sets in these hypergraphs, revealing structural connections in countable models of small theories, are established. The key role of graph-theoretic objects in constructions of Ehrenfeucht theories is proved. Using hypergraph constructions, a classification of complete first-order theories with finite Rudin–Keisler preorders is generalized to the class of all small theories.     

Small stable generic graphs with infinite weight. Bipartite digraphs

Grounding on Herwig’s generic construction that modifies Hrushovski’s construction, we give some examples of the small stable theories of bipartite digraphs with infinite weight.