7 found
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Mariya I. Soskova [6]Mariya Ivanova Soskova [1]
  1.  28
    How Enumeration Reducibility Yields Extended Harrington Non-Splitting.Mariya I. Soskova & S. Barry Cooper - 2008 - Journal of Symbolic Logic 73 (2):634 - 655.
  2.  6
    A Non-Splitting Theorem in the Enumeration Degrees.Mariya Ivanova Soskova - 2009 - Annals of Pure and Applied Logic 160 (3):400-418.
    We complete a study of the splitting/non-splitting properties of the enumeration degrees below by proving an analog of Harrington’s non-splitting theorem for the enumeration degrees. We show how non-splitting techniques known from the study of the c.e. Turing degrees can be adapted to the enumeration degrees.
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  3.  23
    The Limitations of Cupping in the Local Structure of the Enumeration Degrees.Mariya I. Soskova - 2010 - Archive for Mathematical Logic 49 (2):169-193.
    We prove that a sequence of sets containing representatives of cupping partners for every nonzero ${\Delta^0_2}$ enumeration degree cannot have a ${\Delta^0_2}$ enumeration. We also prove that no subclass of the ${\Sigma^0_2}$ enumeration degrees containing the nonzero 3-c.e. enumeration degrees can be cupped to ${\mathbf{0}_e'}$ by a single incomplete ${\Sigma^0_2}$ enumeration degree.
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  4.  7
    Cupping and Definability in the Local Structure of the Enumeration Degrees.Hristo Ganchev & Mariya I. Soskova - 2012 - Journal of Symbolic Logic 77 (1):133-158.
    We show that every splitting of ${0}_{\mathrm{e}}^{\prime }$ in the local structure of the enumeration degrees, $$\mathcal{G}_{e} , contains at least one low-cuppable member. We apply this new structural property to show that the classes of all $\mathcal{K}$ -pairs in $\mathcal{G}_{e}$ , all downwards properly ${\mathrm{\Sigma }}_{2}^{0}$ enumeration degrees and all upwards properly ${\mathrm{\Sigma }}_{2}^{0}$ enumeration degrees are first order definable in $\mathcal{G}_{e}$.
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  5.  4
    Enumeration $1$-Genericity in the Local Enumeration Degrees. [REVIEW]Liliana Badillo, Charles M. Harris & Mariya I. Soskova - 2018 - Notre Dame Journal of Formal Logic 59 (4):461-489.
    We discuss a notion of forcing that characterizes enumeration 1-genericity, and we investigate the immunity, lowness, and quasiminimality properties of enumeration 1-generic sets and their degrees. We construct an enumeration operator Δ such that, for any A, the set ΔA is enumeration 1-generic and has the same jump complexity as A. We deduce from this and other recent results from the literature that not only does every degree a bound an enumeration 1-generic degree b such that a'=b', but also that, (...))
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  6.  4
    Density of the Cototal Enumeration Degrees.Joseph S. Miller & Mariya I. Soskova - 2018 - Annals of Pure and Applied Logic 169 (5):450-462.
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  7.  7
    The Automorphism Group of the Enumeration Degrees.Mariya I. Soskova - 2016 - Annals of Pure and Applied Logic 167 (10):982-999.