Degrees containing members of thin Π10 classes are dense and co-dense

Journal of Mathematical Logic 18 (1):1850001 (2018)

Abstract
In [Countable thin Π10 classes, Ann. Pure Appl. Logic 59 79–139], Cenzer, Downey, Jockusch and Shore proved the density of degrees containing members of countable thin Π10 classes. In the same paper, Cenzer et al. also proved the existence of degrees containing no members of thin Π10 classes. We will prove in this paper that the c.e. degrees containing no members of thin Π10 classes are dense in the c.e. degrees. We will also prove that the c.e. degrees containing members of thin Π10 classes are dense in the c.e. degrees, improving the result of Cenzer et al. mentioned above. Thus, we obtain a new natural subclass of c.e. degrees which are both dense and co-dense in the c.e. degrees, while the other such class is the class of branching c.e. degrees 113–130] for nonbranching degrees and [T. A. Slaman, The density of infima in the recursively enumerable degrees, Ann. Pure Appl. Logic 52 (19...
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DOI 10.1142/S0219061318500010
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References found in this work BETA

Effective Content of Field Theory.G. Metakides & A. Nerode - 1979 - Annals of Mathematical Logic 17 (3):289-320.
Countable Algebra and Set Existence Axioms.H. M. Friedman - 1983 - Annals of Pure and Applied Logic 25 (2):141.
The Density of Infima in the Recursively Enumerable Degrees.Theodore A. Slaman - 1991 - Annals of Pure and Applied Logic 52 (1-2):155-179.
The Density of the Nonbranching Degrees.Peter A. Fejer - 1983 - Annals of Pure and Applied Logic 24 (2):113-130.

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