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  1.  14
    Extended Order-Generic Queries.Oleg V. Belegradek, Alexei P. Stolboushkin & Michael A. Taitslin - 1999 - Annals of Pure and Applied Logic 97 (1-3):85-125.
    We consider relational databases organized over an ordered domain with some additional relations — a typical example is the ordered domain of rational numbers together with the operation of addition. In the focus of our study are the first-order queries that are invariant under order-preserving “permutations” — such queries are called order-generic. It has recently been discovered that for some domains order-generic FO queries fail to express more than pure order queries. For example, every order-generic FO query over rational numbers (...)
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  2.  11
    The Model Theory of Unitriangular Groups.Oleg V. Belegradek - 1994 - Annals of Pure and Applied Logic 68 (3):225-261.
    he model theory of groups of unitriangular matrices over rings is studied. An important tool in these studies is a new notion of a quasiunitriangular group. The models of the theory of all unitriangular groups are algebraically characterized; it turns out that all they are quasiunitriangular groups. It is proved that if R and S are domains or commutative associative rings then two quasiunitriangular groups over R and S are isomorphic only if R and S are isomorphic or antiisomorphic. This (...)
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  3.  33
    On Minimal Structures.Oleg V. Belegradek - 1998 - Journal of Symbolic Logic 63 (2):421-426.
    For any countable transitive complete theory T with infinite models and the finite model property, we construct a minimal structure M such that the theory of M is small if and only if T is small, and is λ-stable if and only if T is λ-stable. This gives a series of new examples of minimal structures.
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  4.  4
    Higman's Embedding Theorem in a General Setting and Its Application to Existentially Closed Algebras.Oleg V. Belegradek - 1996 - Notre Dame Journal of Formal Logic 37 (4):613-624.
    For a quasi variety of algebras K, the Higman Theorem is said to be true if every recursively presented K-algebra is embeddable into a finitely presented K-algebra; the Generalized Higman Theorem is said to be true if any K-algebra which is recursively presented over its finitely generated subalgebra is embeddable into a K-algebra which is finitely presented over this subalgebra. We suggest certain general conditions on K under which the Higman Theorem implies the Generalized Higman Theorem; a finitely generated K-algebra (...)
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