28 found
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  1.  55
    Completely mitotic R.E. degrees.R. G. Downey & T. A. Slaman - 1989 - Annals of Pure and Applied Logic 41 (2):119-152.
  2.  17
    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.
  3.  44
    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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  4.  29
    Minimal degrees recursive in 1-generic degrees.C. T. Chong & R. G. Downey - 1990 - Annals of Pure and Applied Logic 48 (3):215-225.
  5.  19
    Recursion theory and ordered groups.R. G. Downey & Stuart A. Kurtz - 1986 - Annals of Pure and Applied Logic 32:137-151.
  6.  29
    Undecidability of L(F∞) and other lattices of r.e. substructures.R. G. Downey - 1986 - Annals of Pure and Applied Logic 32:17-26.
  7.  23
    Maximal theories.R. G. Downey - 1987 - Annals of Pure and Applied Logic 33 (C):245-282.
  8.  41
    Automorphisms of supermaximal subspaces.R. G. Downey & G. R. Hird - 1985 - Journal of Symbolic Logic 50 (1):1-9.
  9.  32
    Splitting properties of R. E. sets and degrees.R. G. Downey & L. V. Welch - 1986 - Journal of Symbolic Logic 51 (1):88-109.
  10.  48
    Decidable subspaces and recursively enumerable subspaces.C. J. Ash & R. G. Downey - 1984 - Journal of Symbolic Logic 49 (4):1137-1145.
    A subspace V of an infinite dimensional fully effective vector space V ∞ is called decidable if V is r.e. and there exists an r.e. W such that $V \oplus W = V_\infty$ . These subspaces of V ∞ are natural analogues of recursive subsets of ω. The set of r.e. subspaces forms a lattice L(V ∞ ) and the set of decidable subspaces forms a lower semilattice S(V ∞ ). We analyse S(V ∞ ) and its relationship with L(V (...)
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  11.  31
    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.
  12.  59
    Effective extensions of linear forms on a recursive vector space over a recursive field.R. G. Downey & Iraj Kalantari - 1985 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (13):193-200.
  13.  55
    Recursively enumerablem- andtt-degrees II: The distribution of singular degrees. [REVIEW]R. G. Downey - 1988 - Archive for Mathematical Logic 27 (2):135-147.
  14.  44
    The universal complementation property.R. G. Downey & J. B. Remmel - 1984 - Journal of Symbolic Logic 49 (4):1125-1136.
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  15.  25
    A note on decompositions of recursively enumerable subspaces.R. G. Downey - 1984 - Mathematical Logic Quarterly 30 (30):465-470.
  16.  19
    Recursively enumerable m- and tt-degrees. I: The quantity of m- degrees.R. G. Downey - 1989 - Journal of Symbolic Logic 54 (2):553-567.
  17. Master Index to Volumes 71-80.K. A. Abrahamson, R. G. Downey, M. R. Fellows, A. W. Apter, M. Magidor, M. I. da ArchangelskyDekhtyar, M. A. Taitslin, M. A. Arslanov & S. Lempp - 1996 - Annals of Pure and Applied Logic 80:293-298.
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  18. A hierarchy of Turing degrees: a transfinite hierarchy of lowness notions in the computably enumerable degrees, unifying classes, and natural definability.R. G. Downey - 2020 - Princeton: Princeton University Press. Edited by Noam Greenberg.
    This book presents new results in computability theory, a branch of mathematical logic and computer science that has become increasingly relevant in recent years. The field's connections with disparate areas of mathematical logic and mathematics more generally have grown deeper, and now have a variety of applications in topology, group theory, and other subfields. This monograph establishes new directions in the field, blending classic results with modern research areas such as algorithmic randomness. The significance of the book lies not only (...)
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  19. Minimal weak truth table degrees and computably enumerable Turing degrees.R. G. Downey - 2020 - Providence, RI: American Mathematical Society. Edited by Keng Meng Ng & Reed Solomon.
    Informal construction -- Formal construction -- Limiting results.
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  20. Parameterized.R. G. Downey & M. R. Fellows - forthcoming - Complexity.
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  21.  30
    Automorphisms and Recursive Structures.R. G. Downey & J. B. Remmel - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (4):339-345.
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  22.  21
    Bases of Supermaximal Subspaces and Steinitz Systems II.R. G. Downey - 1986 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (13-16):203-210.
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  23.  18
    Sound, totally sound, and unsound recursive equivalence types.R. G. Downey - 1986 - Annals of Pure and Applied Logic 31:1-20.
  24.  11
    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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  25.  11
    Bases of Supermaximal Subspaces and Steinitz Systems II.R. G. Downey - 1986 - Mathematical Logic Quarterly 32 (13‐16):203-210.
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  26.  10
    Automorphisms and Recursive Structures.R. G. Downey & J. B. Remmel - 1987 - Mathematical Logic Quarterly 33 (4):339-345.
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  27.  32
    Intervals and sublattices of the r.e. weak truth table degrees, part II: Nonbounding.R. G. Downey - 1989 - Annals of Pure and Applied Logic 44 (3):153-172.
  28.  30
    A Note on Decompositions of Recursively Enumerable Subspaces.R. G. Downey - 1984 - Mathematical Logic Quarterly 30 (30):465-470.