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The n-r.E. Degrees: Undecidability and σ1 substructures
Journal of Mathematical Logic 12 (1):1250005- (2012)
Abstract
We study the global properties of [Formula: see text], the Turing degrees of the n-r.e. sets. In Theorem 1.5, we show that the first order of [Formula: see text] is not decidable. In Theorem 1.6, we show that for any two n and m with n < m, [Formula: see text] is not a Σ1-substructure of [Formula: see text].Other Versions
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Citations of this work
Weak Density and Nondensity among Transfinite Levels of the Ershov Hierarchy.Yong Liu & Cheng Peng - 2020 - Notre Dame Journal of Formal Logic 61 (4):521-536.
References found in this work
Trial and error predicates and the solution to a problem of Mostowski.Hilary Putnam - 1965 - Journal of Symbolic Logic 30 (1):49-57.
A minimal pair of recursively enumerable degrees.C. E. M. Yates - 1966 - Journal of Symbolic Logic 31 (2):159-168.
The d.r.e. degrees are not dense.S. Barry Cooper, Leo Harrington, Alistair H. Lachlan, Steffen Lempp & Robert I. Soare - 1991 - Annals of Pure and Applied Logic 55 (2):125-151.
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