21 citations · 59 across the 25 of their papers we have counts for
30 papers
Kinds of preservations for properties
Temurboy E. Rajabov, Sergey V. Sudoplatov
We study possibilities of preservations for properties, their links and related connections between semantic and syntactic ones, both in general and as characterizations for subalg…
Expansions and restrictions of structures and theories, their hierarchies
Sergey V. Sudoplatov
We introduce and study some general principles and hierarchical properties of expansions and restrictions of structures and their theories The general approach is applied to descri…
Spherically orderable groups
Sergey V. Sudoplatov
We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of thes…
Variations of rigidity
Sergey V. Sudoplatov
We study possibilities for semantic and syntactic rigidity, i.e., the rigidity with respect to automorphism group and with respect to definable closure. Variations of rigidity and…
Algebraic closures and their variations
Sergey V. Sudoplatov
We study possibilities for algebraic closures, differences between definable and algebraic closures in first-order structures, and variations of these closures with respect to the…
Spherical orders, properties and countable spectra of their theories
Beibut Sh. Kulpeshov, Sergey V. Sudoplatov
We study semantic and syntactic properties of spherical orders and their elementary theories, including finite and dense orders and their theories. It is shown that theories of den…
Arities and aritizabilities of group, monoid and groupoid theories
Inessa I. Pavlyuk, Sergey V. Sudoplatov
We study applications of a general approach for arities and arizabilities of theories to group and monoid theories. It is proved that a theory of a group is aritizable if and o…
Almost -ary and almost -aritizable theories
Sergey V. Sudoplatov
We study possibilities for almost -ary and -aritizable theories. Their dynamics both in general case, for -categorical theories, and with respect to operations for theorie…
Arities and aritizabilities of first-order theories
Sergey V. Sudoplatov
We study and describe possibilities for arities of elementary theories and of their expansions. Links for arities with respect to Boolean algebras, to disjoint unions and to compos…
Formulas and properties
Sergey V. Sudoplatov
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degree…
Definable families of theories, related calculi and ranks
Nurlan Markhabatov, Sergey Sudoplatov
We consider sentence-definable and diagram-definable subfamilies of given families of theories, calculi for these subfamilies, as well dynamics and characteristics of these subfami…
Ranks for families of all theories of given languages
Nurlan Markhabatov, Sergey Sudoplatov
For families of all theories of arbitrary given languages we describe ranks and degrees. In particular, we characterize (non-)totally transcendental families. We apply these charac…
Approximations of theories
Sergey Sudoplatov
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with fini…
Ranks for families of theories and their spectra
Sergey Sudoplatov
We define ranks and degrees for families of theories, similar to Morley rank and degree, as well as Cantor-Bendixson rank and degree, and the notion of totally transcendental famil…
On freedom and independence in hypergraphs of models of theories
Beibut Kulpeshov, Sergey Sudoplatov
Notions of freedom and independence for hypergraphs of models of a theory are defined. Properties of these notions and their applications to some natural classes of theories are st…
On structures in hypergraphs of models of a theory
Beibut Kulpeshov, Sergey Sudoplatov
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a th…
Distributions of countable models of disjoint unions of Ehrenfeucht theories
Sergey Sudoplatov
We describe Rudin-Keisler preorders and distribution functions of numbers of limit models for disjoint unions of Ehrenfeucht theories. Decomposition formulas for these distribution…
On relative separability in hypergraphs of models of theories
Beibut Kulpeshov, Sergey Sudoplatov
In the paper, notions of relative separability for hypergraphs of models of a theory are defined. Properties of these notions and applications to ordered theories are studied: char…
Distributions of countable models of quite o-minimal Ehrenfeucht theories
Beibut Kulpeshov, Sergey Sudoplatov
We describe Rudin-Keisler preorders and distribution functions of numbers of limit models for quite o-minimal Ehrenfeucht theories. Decomposition formulas for these distributions a…
On semilattices and lattices for families of theories
Sergey V. Sudoplatov
We define and study semilattices and lattices for -closed families of theories. Properties of these semilattices and lattices are investigated. It is shown that lattices for fam…
Combinations related to classes of finite and countably categorical structures and their theories
Sergey V. Sudoplatov
We consider and characterize classes of finite and countably categorical structures and their theories preserved under -operators and -operators. We describe -spectra and…
Relative e-spectra and relative closures for families of theories
Sergey V. Sudoplatov
We define the notions of relative -spectra, with respect to -operators, relative closures, and relative generating sets. We study properties connected with relative -spect…
Closures and generating sets related to combinations of structures
Sergey V. Sudoplatov
We investigate closure operators and describe their properties for -combinations and -combinations of structures and their theories. We prove, for -combinations, that the…
Combinations of structures
Sergey V. Sudoplatov
We investigate combinations of structures by families of structures relative to families of unary predicates and equivalence relations. Conditions preserving -categoricity and E…