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  1. On Extensions of Embeddings Into the Enumeration Degrees of the -Sets.Steffen Lempp, Theodore A. Slaman & Andrea Sorbi - 2005 - Journal of Mathematical Logic 5 (02):247-298.
    We give an algorithm for deciding whether an embedding of a finite partial order [Formula: see text] into the enumeration degrees of the [Formula: see text]-sets can always be extended to an embedding of a finite partial order [Formula: see text].
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  • The Π₃-Theory of the [Image] -Enumeration Degrees Is Undecidable.Thomas F. Kent - 2006 - Journal of Symbolic Logic 71 (4):1284 - 1302.
    We show that in the language of {≤}, the Π₃-fragment of the first order theory of the $\Sigma _{2}^{0}$-enumeration degrees is undecidable. We then extend this result to show that the Π₃-theory of any substructure of the enumeration degrees which contains the $\Delta _{2}^{0}$-degrees is undecidable.
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  • Interpreting True Arithmetic in the Δ 0 2 -Enumeration Degrees.Thomas F. Kent - 2010 - Journal of Symbolic Logic 75 (2):522-550.
    We show that there is a first order sentence φ(x; a, b, l) such that for every computable partial order.
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  • Branching in the $${\Sigma^0_2}$$ -Enumeration Degrees: A New Perspective. [REVIEW]Maria L. Affatato, Thomas F. Kent & Andrea Sorbi - 2008 - Archive for Mathematical Logic 47 (3):221-231.
    We give an alternative and more informative proof that every incomplete ${\Sigma^{0}_{2}}$ -enumeration degree is the meet of two incomparable ${\Sigma^{0}_{2}}$ -degrees, which allows us to show the stronger result that for every incomplete ${\Sigma^{0}_{2}}$ -enumeration degree a, there exist enumeration degrees x 1 and x 2 such that a, x 1, x 2 are incomparable, and for all b ≤ a, b = (b ∨ x 1 ) ∧ (b ∨ x 2 ).
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  • 2-Minimality, Jump Classes and a Note on Natural Definability.Mingzhong Cai - 2014 - Annals of Pure and Applied Logic 165 (2):724-741.
    We show that there is a generalized high degree which is a minimal cover of a minimal degree. This is the highest jump class one can reach by finite iterations of minimality. This result also answers an old question by Lerman.
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  • Bounding Nonsplitting Enumeration Degrees.Thomas F. Kent & Andrea Sorbi - 2007 - Journal of Symbolic Logic 72 (4):1405 - 1417.
    We show that every nonzero $\Sigma _{2}^{0}$ enumeration degree bounds a nonsplitting nonzero enumeration degree.
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