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  1. Splitting theorems and the jump operator.R. G. Downey & Richard A. Shore - 1998 - Annals of Pure and Applied Logic 94 (1-3):45-52.
    We investigate the relationship of the degrees of splittings of a computably enumerable set and the degree of the set. We prove that there is a high computably enumerable set whose only proper splittings are low 2.
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  • Splitting theorems in recursion theory.Rod Downey & Michael Stob - 1993 - Annals of Pure and Applied Logic 65 (1):1-106.
    A splitting of an r.e. set A is a pair A1, A2 of disjoint r.e. sets such that A1 A2 = A. Theorems about splittings have played an important role in recursion theory. One of the main reasons for this is that a splitting of A is a decomposition of A in both the lattice, , of recursively enumerable sets and in the uppersemilattice, R, of recursively enumerable degrees . Thus splitting theor ems have been used to obtain results about (...)
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