10 found
Order:
Disambiguations
Oleg Belegradek [9]Oleg V. Belegradek [4]
  1. Quasi-o-Minimal Structures.Oleg Belegradek, Ya'Acov Peterzil & Frank Wagner - 2000 - Journal of Symbolic Logic 65 (3):1115-1132.
    A structure (M, $ ,...) is called quasi-o-minimal if in any structure elementarily equivalent to it the definable subsets are exactly the Boolean combinations of 0-definable subsets and intervals. We give a series of natural examples of quasi-o-minimal structures which are not o-minimal; one of them is the ordered group of integers. We develop a technique to investigate quasi-o-minimality and use it to study quasi-o-minimal ordered groups (possibly with extra structure). Main results: any quasi-o-minimal ordered group is abelian; any quasi-o-minimal (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  2.  5
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  3.  6
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  4.  7
    Coset-Minimal Groups.Oleg Belegradek, Viktor Verbovskiy & Frank O. Wagner - 2003 - Annals of Pure and Applied Logic 121 (2-3):113-143.
    A totally ordered group G is called coset-minimal if every definable subset of G is a finite union of cosets of definable subgroups intersected with intervals with endpoints in G{±∞}. Continuing work in Belegradek et al. 1115) and Point and Wagner 261), we study coset-minimality, as well as two weak versions of the notion: eventual and ultimate coset-minimality. These groups are abelian; an eventually coset-minimal group, as a pure ordered group, is an ordered abelian group of finite regular rank. Any (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  5.  21
    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.
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  6.  19
    Homogeneity in Relatively Free Groups.Oleg Belegradek - 2012 - Archive for Mathematical Logic 51 (7-8):781-787.
    We prove that any torsion-free, residually finite relatively free group of infinite rank is not ${\aleph_1}$ -homogeneous. This generalizes Sklinos’ result that a free group of infinite rank is not ${\aleph_1}$ -homogeneous, and, in particular, gives a new simple proof of that result.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  7.  3
    In Memoriam: Mikhail A. Taitslin 1936–2013.Oleg Belegradek & Boris Zilber - 2014 - Bulletin of Symbolic Logic 20 (1):99-102.
  8.  4
    Semi-Bounded Relations in Ordered Modules.Oleg Belegradek - 2004 - Journal of Symbolic Logic 69 (2):499 - 517.
    A relation on a linearly ordered structure is called semi-bounded if it is definable in an expansion of the structure by bounded relations. We study ultimate behavior of semi-bounded relations in an ordered module M over an ordered commutative ring R such that M/rM is finite for all nonzero r $\epsilon$ R. We consider M as a structure in the language of ordered R-modules augmented by relation symbols for the submodules rM, and prove several quantifier elimination results for semi-bounded relations (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  9.  1
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  10.  1
    The Space of Minimal Structures.Oleg Belegradek - 2014 - Mathematical Logic Quarterly 60 (1-2):40-53.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography