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RECOGNIZING STRONG RANDOM REALS

RECOGNIZING STRONG RANDOM REALS,10.1017/S1755020308080076,Review of Symbolic Logic,DANIEL OSHERSON,SCOTT WEINSTEIN

RECOGNIZING STRONG RANDOM REALS   (Citations: 2)
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The class of strong random reals can be defined via a natural conception of effective null set. We show that the same class is also characterized by a learning-theoretic criterion of 'recognizability'.
Journal: Review of Symbolic Logic - REV SYMB LOG , vol. 1, no. 01, 2008
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    • ...Strong randomness [8,17] has various nice characterisations, in particular the following: A is strongly random iff A is Martin-L¨ of random and forms a minimal pair with K with respect to Turing reducibility [4, Footnote 2]. For these notions, in order to quantify the degree of non-randomness of a sequence, one studies from which value f (m) onwards all initial segments can be compressed by m bits...

    Rupert Hölzlet al. Initial Segment Complexities of Randomness Notions

    • ...Furthermore, a set is called “weakly 2-random” [20] or “strongly random” [24] if and only if it is Martin-L¨of random and forms a minimal pair with the halting problem...

    Johanna N. Y. Franklinet al. Relativizations of Randomness and Genericity Notions

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