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  1. The α-finite injury method.G. E. Sacks & S. G. Simpson - 1972 - Annals of Mathematical Logic 4 (4):343-367.
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  • The universal splitting property. II.M. Lerman & J. B. Remmel - 1984 - Journal of Symbolic Logic 49 (1):137-150.
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  • Mitotic recursively enumerable sets.Richard E. Ladner - 1973 - Journal of Symbolic Logic 38 (2):199-211.
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  • Completely mitotic c.e. degrees and non-jump inversion.Evan J. Griffiths - 2005 - Annals of Pure and Applied Logic 132 (2-3):181-207.
    A completely mitotic computably enumerable degree is a c.e. degree in which every c.e. set is mitotic, or equivalently in which every c.e. set is autoreducible. There are known to be low, low2, and high completely mitotic degrees, though the degrees containing non-mitotic sets are dense in the c.e. degrees. We show that there exists an upper cone of c.e. degrees each of which contains a non-mitotic set, and that the completely mitotic c.e. degrees are nowhere dense in the c.e. (...)
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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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  • 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.
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  • Splitting properties of R. E. sets and degrees.R. G. Downey & L. V. Welch - 1986 - Journal of Symbolic Logic 51 (1):88-109.
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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.
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  • 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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  • Kolmogorov complexity and computably enumerable sets.George Barmpalias & Angsheng Li - 2013 - Annals of Pure and Applied Logic 164 (12):1187-1200.
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  • Algorithmic Randomness and Measures of Complexity.George Barmpalias - 2013 - Bulletin of Symbolic Logic 19 (3):318-350.
    We survey recent advances on the interface between computability theory and algorithmic randomness, with special attention on measures of relative complexity. We focus on reducibilities that measure the initial segment complexity of reals and the power of reals to compress strings, when they are used as oracles. The results are put into context and several connections are made with various central issues in modern algorithmic randomness and computability.
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  • Degree theoretical splitting properties of recursively enumerable sets.Klaus Ambos-Spies & Peter A. Fejer - 1988 - Journal of Symbolic Logic 53 (4):1110-1137.
    A recursively enumerable splitting of an r.e. setAis a pair of r.e. setsBandCsuch thatA=B∪CandB∩C= ⊘. Since for such a splitting degA= degB∪ degC, r.e. splittings proved to be a quite useful notion for investigations into the structure of the r.e. degrees. Important splitting theorems, like Sacks splitting [S1], Robinson splitting [R1] and Lachlan splitting [L3], use r.e. splittings.Since each r.e. splitting of a set induces a splitting of its degree, it is natural to study the relation between the degrees of (...)
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