Abstract
We settle a series of questions first raised by Yates at the Jerusalem (1968) Colloquium on Mathematical Logic by characterizing the initial segments of the degrees of unsolvability of size ℵ1: Every upper semi-lattice of size ℵ1 with zero, in which every element has at most countably many predecessors, is isomorphic to an initial segment of the Turing degrees.
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The second author was partially supported by a grant from the NSF. The research was carried out while he was on sabbatical leave from Cornell University and a Visiting Professor at the Hebrew University, Jersalem. He would like to thank the Hebrew University and in particular the logicians there for their hospitality.
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Abraham, U., Shore, R.A. Initial segments of the degrees of size ℵ1 . Israel J. Math. 53, 1–51 (1986). https://doi.org/10.1007/BF02772668
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DOI: https://doi.org/10.1007/BF02772668