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Просмотр по теме "Computability"

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  • Computability on linear orderings enriched with predicates 
    Alaev P.; Thurber J.; Frolov A. (2009)
    Let L be a quasidiscrete linear ordering. We specify some conditions for the existence of a computable presentation for L or for the structure (L, adj), where adj(x, y) is a predicate distinguishing adjacent elements. © ...
  • Degree Spectra for Transcendence in Fields 
    Kalimullin I.; Miller R.; Schoutens H. (2019)
    © 2019, Springer Nature Switzerland AG. We show that for both the unary relation of transcendence and the finitary relation of algebraic independence on a field, the degree spectra of these relations may consist of any ...
  • Degrees of categoricity of computable structures 
    Fokina E.; Kalimullin I.; Miller R. (2009)
    Defining the degree of categoricity of a computable structure M to be the least degree d for which M is d-computably categorical, we investigate which Turing degrees can be realized as degrees of categoricity. We show that ...
  • Graphs are not universal for online computability 
    Downey R.; Harrison-Trainor M.; Kalimullin I.; Melnikov A.; Turetsky D. (2020)
    © 2020 Elsevier Inc. We show that structures with only one binary function symbol are universal for “online” (punctual) computable structures. In contrast, we give a description of punctually categorical graphs which implies ...
  • Initial segments of computable linear orders with additional computable predicates 
    Zubkov M. (2009)
    We study computable linear orders with computable neighborhood and block predicates. In particular, it is proved that there exists a computable linear order with a computable neighborhood predicate, having a -initial segment ...
  • Low linear orderings 
    Frolov A. (2012)
    We say that L is weakly η-like if L/∼ is isomorphic to the natural ordering of rational numbers. We construct a computable presentation of any low weakly η-like linear ordering with no strongly η-like interval. Also we ...
  • Quasi-completeness and functions without fixed-points 
    Batyrshin I. (2006)
    We prove a completeness criterion for quasi-reducibility and generalize it to higher levels of the arithmetical hierarchy. As an application of the criterion we obtain Q-completeness of the set of all pairs (x, n) such ...
  • Spectra of algebraic fields and subfields 
    Frolov A.; Kalimullin I.; Miller R. (2009)
    An algebraic field extension of ℚ or ℤ/(p) may be regarded either as a structure in its own right, or as a subfield of its algebraic closure F (either ℚ or ℤ/(p)). We consider the Turing degree spectrum of F in both cases, ...
  • Spectra of high n and non-low n degrees 
    Frolov A.; Kalimullin I.; Harizanov V.; Kudinov O.; Miller R. (2012)
    We survey known results on spectra of structures and on spectra of relations on computable structures, asking when the set of all highn degrees can be such a spectrum, and likewise for the set of non-low n degrees. We then ...
  • Splitting and nonsplitting in the Σ2 0 enumeration degrees 
    Arslanov M.; Cooper S.; Kalimullin I.; Soskova M. (2011)
    This paper continues the project, initiated in (Arslanov, Cooper and Kalimullin 2003) [3], of describing general conditions under which relative splittings are derivable in the local structure of the enumeration degrees, ...

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