Goldstern, Martin The complexity of uniform distribution. (English) Zbl 0820.03031 Math. Slovaca 44, No. 5, 491-500 (1994). Summary: We investigate the notion of testable sequence which was proposed by R. Winkler [ibid. 43, No. 4, 493-512 (1993; Zbl 0813.65001)], and we show that the set of uniformly distributed sequences is \(\Pi^ 0_ 3\)- complete, hence not refutable. Cited in 2 Documents MSC: 03D80 Applications of computability and recursion theory 11B50 Sequences (mod \(m\)) 11K45 Pseudo-random numbers; Monte Carlo methods 03D20 Recursive functions and relations, subrecursive hierarchies 03E15 Descriptive set theory 03D55 Hierarchies of computability and definability Keywords:arithmetical hierarchy; testable sequence; uniformly distributed sequences Citations:Zbl 0813.65001 PDFBibTeX XMLCite \textit{M. Goldstern}, Math. Slovaca 44, No. 5, 491--500 (1994; Zbl 0820.03031) Full Text: EuDML References: [1] MOSCHOVAKIS Y. N.: Descriptive Set Theory. Stud. Logic Found. Math. 100, North-Holland, Amsterdam-New York-Oxford, 1980. · Zbl 0433.03025 [2] ROGERS H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, London, 1967. · Zbl 0183.01401 [3] WINKLER R.: Some remarks on pseudorandom sequences. Math. Slovaca 43 (1993), 493-512. · Zbl 0813.65001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.