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22

APAL
2011

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Upper bounds on ideals in the computably enumerable Turing degrees

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Upper bounds on ideals in the computably enumerable Turing degrees

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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

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APAL 2011 | Proper Σ0 | Software Engineering | Turing Degrees | Upper Bound |

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Added	12 May 2011
Updated	12 May 2011
Type	Journal
Year	2011
Where	APAL
Authors	George Barmpalias, André Nies

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