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  1. Completeness, Compactness, Effective Dimensions.Stephen Binns - 2013 - Mathematical Logic Quarterly 59 (3):206-218.
  • Calibrating Randomness.Rod Downey, Denis R. Hirschfeldt, André Nies & Sebastiaan A. Terwijn - 2006 - Bulletin of Symbolic Logic 12 (3):411-491.
    We report on some recent work centered on attempts to understand when one set is more random than another. We look at various methods of calibration by initial segment complexity, such as those introduced by Solovay [125], Downey, Hirschfeldt, and Nies [39], Downey, Hirschfeldt, and LaForte [36], and Downey [31]; as well as other methods such as lowness notions of Kučera and Terwijn [71], Terwijn and Zambella [133], Nies [101, 100], and Downey, Griffiths, and Reid [34]; higher level randomness notions (...)
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  • Relative Kolmogorov Complexity and Geometry.Stephen Binns - 2011 - Journal of Symbolic Logic 76 (4):1211-1239.
    We use the notions of effective dimension and Kolmogorov complexity to describe a geometry on the set of infinite binary sequences. Geometric concepts that we define and use include angle, projections and scalar multiplication. A question related to compressibility is addressed using these ideas.
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  • Avoiding Effective Packing Dimension 1 Below Array Noncomputable C.E. Degrees.Rod Downey & Jonathan Stephenson - 2018 - Journal of Symbolic Logic 83 (2):717-739.
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