Lattice initial segments of the Turing degrees

Details Lattice initial segments of the Turing degrees Lattice initial segments of the Turing degrees

2009-01-25

arxiv.org/abs/0901.3876v2

Mathematics

Logic

Doctoral dissertation, Logic and the Methodology of Science, University of California, Berkeley, 2002

Scientific paper

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".

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