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  1. Structural Interactions of the Recursively Enumerable T- and W-Degrees.R. G. Downey & M. Stob - 1986 - Annals of Pure and Applied Logic 31:205-236.
  • Intervals and Sublattices of the R.E. Weak Truth Table Degrees, Part I: Density.R. G. Downey - 1989 - Annals of Pure and Applied Logic 41 (1):1-26.
  • 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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  • Completely Mitotic R.E. Degrees.R. G. Downey & T. A. Slaman - 1989 - Annals of Pure and Applied Logic 41 (2):119-152.
  • Classifications of Degree Classes Associated with R.E. Subspaces.R. G. Downey & J. B. Remmel - 1989 - Annals of Pure and Applied Logic 42 (2):105-124.
    In this article we show that it is possible to completely classify the degrees of r.e. bases of r.e. vector spaces in terms of weak truth table degrees. The ideas extend to classify the degrees of complements and splittings. Several ramifications of the classification are discussed, together with an analysis of the structure of the degrees of pairs of r.e. summands of r.e. spaces.
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  • A Contiguous Nonbranching Degree.Rod Downey - 1989 - Mathematical Logic Quarterly 35 (4):375-383.
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