Upper bounds on ideals in the computably enumerable Turing degrees

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Annals of Pure and Applied Logic 162 (6):465-473 (2011)
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Abstract

We study ideals in the computably enumerable Turing degrees, and their upper bounds. Every proper ideal in the c.e. Turing degrees has an incomplete upper bound. It follows that there is no prime ideal in the c.e. Turing degrees. This answers a question of Calhoun [2]. Every proper ideal in the c.e. Turing degrees has a low2 upper bound. Furthermore, the partial order of ideals under inclusion is dense

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10.1016/j.apal.2010.12.005

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Citations of this work

Algorithmic Randomness and Measures of Complexity.George Barmpalias - 2013 - Bulletin of Symbolic Logic 19 (3):318-350.

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References found in this work

Randomness and computability: Open questions.Joseph S. Miller & André Nies - 2006 - Bulletin of Symbolic Logic 12 (3):390-410.
Lowness properties and approximations of the jump.Santiago Figueira, André Nies & Frank Stephan - 2008 - Annals of Pure and Applied Logic 152 (1):51-66.
Benign cost functions and lowness properties.Noam Greenberg & André Nies - 2011 - Journal of Symbolic Logic 76 (1):289 - 312.
Low upper bounds of ideals.Antonín Kučera & Theodore A. Slaman - 2009 - Journal of Symbolic Logic 74 (2):517-534.
Parameter definability in the recursively enumerable degrees.André Nies - 2003 - Journal of Mathematical Logic 3 (01):37-65.

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