Bjørn Kjos-Hanssen
Published 2009-01-25, updated 2011-07-13Version 2
We characterize the isomorphism types of principal ideals of the Turing degrees below 0' that are lattices as the lattices with a Sigma-0-3 presentation, by showing that each Sigma-0-3 presentable bounded upper semilattice is isomorphic to such a principal ideal. We get a similar result for the Turing degrees below any degree above 0".
Comments: Doctoral dissertation, Logic and the Methodology of Science, University of California, Berkeley, 2002
Coarse computability, the density metric, Hausdorff distances between Turing degrees, perfect trees, and reverse mathematics
Lattice initial segments of the hyperdegrees
Determinacy and Fast-growing Sequences of Turing Degrees
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