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  1. No Access

    Chapter

    Bounded Randomness

    We introduce some new variations of the notions of being Martin-Löf random where the tests are all clopen sets. We explore how these randomness notions relate to classical randomness notions and to degrees of ...

    Paul Brodhead, Rod Downey, Keng Meng Ng in Computation, Physics and Beyond (2012)

  2. No Access

    Chapter and Conference Paper

    Numberings and Randomness

    We prove various results on effective numberings and Friedberg numberings of families related to algorithmic randomness. The family of all Martin-Löf random left-computably enumerable reals has a Friedberg num...

    Paul Brodhead, Bjørn Kjos-Hanssen in Mathematical Theory and Computational Practice (2009)

  3. No Access

    Chapter and Conference Paper

    The Strength of the Grätzer-Schmidt Theorem

    The Grätzer-Schmidt theorem of lattice theory states that each algebraic lattice is isomorphic to the congruence lattice of an algebra. A lattice is algebraic if it is complete and generated by its compact ele...

    Paul Brodhead, Bjørn Kjos-Hanssen in Mathematical Theory and Computational Practice (2009)

  4. No Access

    Article

    Algorithmic randomness of continuous functions

    We investigate notions of randomness in the space \({{\mathcal C}(2^{\mathbb N})}\) of continuous functions on ...

    George Barmpalias, Paul Brodhead, Douglas Cenzer… in Archive for Mathematical Logic (2008)

  5. No Access

    Article

    Effectively closed sets and enumerations

    An effectively closed set, or \({\Pi^{0}_{1}}\) class, may viewed as the set of infinite paths through a computable t...

    Paul Brodhead, Douglas Cenzer in Archive for Mathematical Logic (2008)

  6. No Access

    Chapter and Conference Paper

    Random Closed Sets

    We investigate notions of randomness in the space \({\mathcal {C}}[2^{\mathbb {N}}]\) of nonempty closed subsets of {0,1}ℕ. A pro...

    Paul Brodhead, Douglas Cenzer… in Logical Approaches to Computational Barriers (2006)