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  1.  24
    Relative Enumerability in the Difference Hierarchy.Marat M. Arslanov, Geoffrey L. Laforte & Theodore A. Slaman - 1998 - Journal of Symbolic Logic 63 (2):411-420.
    We show that the intersection of the class of 2-REA degrees with that of the ω-r.e. degrees consists precisely of the class of d.r.e. degrees. We also include some applications and show that there is no natural generalization of this result to higher levels of the REA hierarchy.
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  2.  39
    Density Results in the Δ 2 0 E-Degrees.Marat M. Arslanov, Iskander Sh Kalimullin & Andrea Sorbi - 2001 - Archive for Mathematical Logic 40 (8):597-614.
    We show that the Δ0 2 enumeration degrees are dense. We also show that for every nonzero n-c. e. e-degree a, with n≥ 3, one can always find a nonzero 3-c. e. e-degree b such that b < a on the other hand there is a nonzero ωc. e. e-degree which bounds no nonzero n-c. e. e-degree.
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  3.  13
    The Ershov Hierarchy.Marat M. Arslanov - 2011 - In S. B. Cooper & Andrea Sorbi (eds.), Computability in Context: Computation and Logic in the Real World. World Scientific.
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  4.  17
    Structural Properties of Q -Degrees of N-C. E. Sets.Marat M. Arslanov, Ilnur I. Batyrshin & R. Sh Omanadze - 2008 - Annals of Pure and Applied Logic 156 (1):13-20.
    In this paper we study structural properties of n-c. e. Q-degrees. Two theorems contain results on the distribution of incomparable Q-degrees. In another theorem we prove that every incomplete Q-degree forms a minimal pair in the c. e. degrees with a Q-degree. In a further theorem it is proved that there exists a c. e. Q-degree that is not half of a minimal pair in the c. e. Q-degrees.
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  5.  4
    On Downey's Conjecture.Marat M. Arslanov, Iskander Sh Kalimullin & Steffen Lempp - 2010 - Journal of Symbolic Logic 75 (2):401-441.
    We prove that the degree structures of the d.c.e. and the 3-c.e. Turing degrees are not elementarily equivalent, thus refuting a conjecture of Downey. More specifically, we show that the following statement fails in the former but holds in the latter structure: There are degrees f > e > d > 0 such that any degree u ≤ f is either comparable with both e and d, or incomparable with both.
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