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Marat Arslanov [6]Marat M. Arslanov [5]M. M. Arslanov [3]M. A. Arslanov [2]
M. Arslanov [2]
  1.  9
    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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  2.  37
    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.  16
    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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  4.  20
    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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  5.  37
    There is No Low Maximal D.C.E. Degree.Marat Arslanov, S. Barry Cooper & Angsheng Li - 2000 - Mathematical Logic Quarterly 46 (3):409-416.
    We show that for any computably enumerable set A and any equation image set L, if L is low and equation image, then there is a c.e. splitting equation image such that equation image. In Particular, if L is low and n-c.e., then equation image is n-c.e. and hence there is no low maximal n-c.e. degree.
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  6.  1
    Archangel&y, DA, Dekhtyar, MI and Taitslin, MA, Linear Logic For.M. A. Arslanov, S. Lempp, R. A. Shore, S. Artemov, V. Krupski, A. Dabrowski, L. S. Moss, R. Parikh, T. Eiter & G. Gottlob - 1996 - Annals of Pure and Applied Logic 78 (1-3):271.
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  7.  61
    There is No Low Maximal D. C. E. Degree– Corrigendum.M. Arslanov & S. B. Cooper - 2004 - Mathematical Logic Quarterly 50 (6):628.
    We give a corrected proof of an extension of the Robinson Splitting Theorem for the d. c. e. degrees.
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  8.  2
    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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  9. Master Index to Volumes 71-80.K. A. Abrahamson, R. G. Downey, M. R. Fellows, A. W. Apter, M. Magidor, M. I. da ArchangelskyDekhtyar, M. A. Taitslin, M. A. Arslanov & S. Lempp - 1996 - Annals of Pure and Applied Logic 80:293-298.
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  10.  10
    Participants and Titles of Lectures.Klaus Ambos-Spies, Marat Arslanov, Douglas Cenzer, Peter Cholak, Chi Tat Chong, Decheng Ding, Rod Downey, Peter A. Fejer, Sergei S. Goncharov & Edward R. Griffor - 1998 - Annals of Pure and Applied Logic 94 (1):3-6.
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  11.  25
    Interpolating D-R.E. And REA Degrees Between R.E. Degrees.Marat Arslanov, Steffen Lempp & Richard A. Shore - 1996 - Annals of Pure and Applied Logic 78 (1-3):29-56.
    We provide three new results about interpolating 2-r.e. or 2-REA degrees between given r.e. degrees: Proposition 1.13. If c h are r.e. , c is low and h is high, then there is an a h which is REA in c but not r.e. Theorem 2.1. For all high r.e. degrees h g there is a properly d-r.e. degree a such that h a g and a is r.e. in h . Theorem 3.1. There is an incomplete nonrecursive r.e. A (...)
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  12. Recursion Theory and Complexity: Proceedings of the Kazan '97 Workshop, Kazan, Russia, July 14-19, 1997.M. M. Arslanov & Steffen Lempp (eds.) - 1999 - W. De Gruyter.
  13.  17
    There is No Low Maximal D. C. E. Degree– Corrigendum.Marat Arslanov, S. Barry Cooper & Angsheng Li - 2004 - Mathematical Logic Quarterly 50 (6):628-636.
    We give a corrected proof of an extension of the Robinson Splitting Theorem for the d. c. e. degrees.
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  14.  37
    The Minimal E-Degree Problem in Fragments of Peano Arithmetic.M. M. Arslanov, C. T. Chong, S. B. Cooper & Y. Yang - 2005 - Annals of Pure and Applied Logic 131 (1-3):159-175.
    We study the minimal enumeration degree problem in models of fragments of Peano arithmetic () and prove the following results: in any model M of Σ2 induction, there is a minimal enumeration degree if and only if M is a nonstandard model. Furthermore, any cut in such a model has minimal e-degree. By contrast, this phenomenon fails in the absence of Σ2 induction. In fact, whether every Σ2 cut has minimal e-degree is independent of the Σ2 bounding principle.
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  15.  1
    The Minimal E-Degree Problem in Fragments of Peano Arithmetic.M. Arslanov, C. Chong, S. Cooper & Y. Yang - 2005 - Annals of Pure and Applied Logic 131 (1-3):159-175.
    We study the minimal enumeration degree problem in models of fragments of Peano arithmetic () and prove the following results: in any model M of Σ2 induction, there is a minimal enumeration degree if and only if M is a nonstandard model. Furthermore, any cut in such a model has minimal e-degree. By contrast, this phenomenon fails in the absence of Σ2 induction. In fact, whether every Σ2 cut has minimal e-degree is independent of the Σ2 bounding principle.
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  16.  4
    Nijmegen, The Netherlands July 27–August 2, 2006.Rodney Downey, Ieke Moerdijk, Boban Velickovic, Samson Abramsky, Marat Arslanov, Harvey Friedman, Martin Goldstern, Ehud Hrushovski, Jochen Koenigsmann & Andy Lewis - 2007 - Bulletin of Symbolic Logic 13 (2).
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