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    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)

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    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)

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    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)