Upper bounds on ideals in the computably enumerable Turing degrees

نویسندگان

George Barmpalias

André Nies

چکیده

We study ideals in the computably enumerable Turing degrees, and their upper bounds. Every proper Σ0 4 ideal in the c.e. Turing degrees has an incomplete upper bound. It follows that there is no Σ0 4 prime ideal in the c.e. Turing degrees. This answers a question of Calhoun (1993) [2]. Every properΣ0 3 ideal in the c.e. Turing degrees has a low2 upper bound. Furthermore, the partial order of Σ0 3 ideals under inclusion is dense. © 2011 Elsevier B.V. All rights reserved.

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