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The problem of identifying the order types of the countable initial segments of the degrees of unsolvability was first tackled by Clifford Spector more than 20 years ago, and has since given rise to a series of papers, In this thesis a complete characterization of these order types is given by proving the following theorem: any countable upper semilattice with least element can be embedded as an initial segment of the degrees. '12 mes parents."doi:10.2307/2272227 fatcat:k3dkdsdxvfat3j2djg2omdtnx4