Embedding of countable orders in Turing degrees
Consider a descending sequence \(\{{\mathbf c}_i\)\} of nonzero Turing degrees in which the reductions \textbf{c}\(_{i+1}\leq{\mathbf c}_i\) can be carried out uniformly in \({\mathbf 0}'\). The author shows that, in fact, the reductions can be carried out uniformly and that there exists a nonzero degree below every \({\mathbf c}_i\). In particular, such a sequence cannot form an initial segment of nonzero degrees.
scientific article; zbMATH DE number 1928328