•  9
    On Cohesive Powers of Linear Orders
    with Valentina Harizanov, Andrey Morozov, Paul Shafer, Alexandra A. Soskova, and Stefan V. Vatev
    Journal of Symbolic Logic 88 (3): 947-1004. 2023.
    Cohesive powersof computable structures are effective analogs of ultrapowers, where cohesive sets play the role of ultrafilters. Let$\omega $,$\zeta $, and$\eta $denote the respective order-types of the natural numbers, the integers, and the rationals when thought of as linear orders. We investigate the cohesive powers of computable linear orders, with special emphasis on computable copies of$\omega $. If$\mathcal {L}$is a computable copy of$\omega $that is computably isomorphic to the usual pre…Read more
  •  14
    Dependence relations in computably rigid computable vector spaces
    with Valentina S. Harizanov and Andrei S. Morozov
    Annals of Pure and Applied Logic 132 (1): 97-108. 2005.
    We construct a computable vector space with the trivial computable automorphism group, but with the dependence relations as complicated as possible, measured by their Turing degrees. As a corollary, we answer a question asked by A.S. Morozov in [Rigid constructive modules, Algebra and Logic, 28 570–583 ; 379–387 ]
  •  7
    Quasimaximality and principal filters isomorphism between
    Archive for Mathematical Logic 43 (3): 415-424. 2004.
    Let I be a quasimaximal subset of a computable basis of the fully efective vector space V ∞ . We give a necessary and sufficient condition for the existence of an isomorphism between the principal filter respectivelly. We construct both quasimaximal sets that satisfy and quasimaximal sets that do not satisfy this condition. With the latter we obtain a negative answer to Question 5.4 posed by Downey and Remmel in [3]
  •  17
    Let I0 be a a computable basis of the fully effective vector space V∞ over the computable field F. Let I be a quasimaximal subset of I0 that is the intersection of n maximal subsets of the same 1-degree up to *. We prove that the principal filter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{L}^{\ast}(V,\…Read more
  • Nomenkulturata
    Universitetsko Izd-Vo "Kliment Okhridski". 1991.