Genericity and UD-random reals

Wesley Calvert, Johanna N.Y. Franklin


Avigad introduced the notion of UD-randomness based in Weyl's 1916 definition of uniform distribution modulo one.  We prove that there exists a weakly 1-random real that is neither UD-random nor weakly 1-generic.  We also show that no 2-generic real can Turing compute a UD-random real.

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Journal of Logic and Analysis ISSN:  1759-9008