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APAL
2011

Upper bounds on ideals in the computably enumerable Turing degrees

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Upper bounds on ideals in the computably enumerable Turing degrees
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 [Cal93]. Every proper Σ0 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.
George Barmpalias, André Nies
Added 12 May 2011
Updated 12 May 2011
Type Journal
Year 2011
Where APAL
Authors George Barmpalias, André Nies
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