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  1. Hristo Ganchev & Mariya Soskova (2012). Interpreting True Arithmetic in the Local Structure of the Enumeration Degrees. Journal of Symbolic Logic 77 (4):1184-1194.
    We show that the theory of the local structure of the enumeration degrees is computably isomorphic to the theory of first order arithmetic. We introduce a novel coding method, using the notion of a K-pair, to code a large class of countable relations.
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  2. Hristo Ganchev & Mariya Soskova (2012). The High/Low Hierarchy in the Local Structure of the Ω-Enumeration Degrees. Annals of Pure and Applied Logic 163 (5):547-566.
  3. Hristo Ganchev & Mariya I. Soskova (2012). Cupping and Definability in the Local Structure of the Enumeration Degrees. 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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  4. Mariya I. Soskova (2010). The Limitations of Cupping in the Local Structure of the Enumeration Degrees. 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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  5. Mariya Ivanova Soskova (2009). A Non-Splitting Theorem in the Enumeration Degrees. 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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  6. George Barmpalias, Andrew E. M. Lewis & Mariya Soskova (2008). Randomness, Lowness and Degrees. Journal of Symbolic Logic 73 (2):559 - 577.
    We say that A ≤LR B if every B-random number is A-random. Intuitively this means that if oracle A can identify some patterns on some real γ. In other words. B is at least as good as A for this purpose. We study the structure of the LR degrees globally and locally (i.e., restricted to the computably enumberable degrees) and their relationship with the Turing degrees. Among other results we show that whenever α in not GL₂ the LR degree of (...)
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  7. George Barmpalias, Andrew Lewis & Mariya Soskova (2008). Randomness, Lowness and Degrees. Journal of Symbolic Logic 73 (2):559-577.
    We say that A≤LRB if every B-random number is A-random. Intuitively this means that if oracle A can identify some patterns on some real γ, oracle B can also find patterns on γ. In other words, B is at least as good as A for this purpose. We study the structure of the LR degrees globally and locally and their relationship with the Turing degrees. Among other results we show that whenever α is not GL2 the LR degree of α (...)
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  8. S. Cooper & Mariya Soskova (2008). How Enumeration Reducibility Yields Extended Harrington Non-Splitting. Journal of Symbolic Logic 73 (2):634-655.
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  9. Mariya I. Soskova & S. Barry Cooper (2008). How Enumeration Reducibility Yields Extended Harrington Non-Splitting. Journal of Symbolic Logic 73 (2):634 - 655.
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