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NORMAL NUMBERS AND COMPLETENESS RESULTS FOR DIFFERENCE SETS

  • KONSTANTINOS A. BEROS (a1)

Abstract

We consider some natural sets of real numbers arising in ergodic theory and show that they are, respectively, complete in the classes ${\cal D}_2 \left( {{\bf{\Pi }}_3^0 } \right)$ and ${\cal D}_\omega \left( {{\bf{\Pi }}_3^0 } \right)$ , that is, the class of sets which are 2-differences (respectively, ω-differences) of ${\bf{\Pi }}_3^0 $ sets.

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[1] Becher, V. and Slaman, T. A., On the normality of numbers in different bases . Journal of the London Mathematical Society, vol. 90 (2014), no. 2, pp. 472494.
[2] Becher, V., Ariel Heiber, P. and Slaman, T., Normal numbers in the Borel hierarchy . Fundamenta Mathematicae, vol. 226 (2014), pp. 6377.
[3] Good, I. J., Normal recurring decimals . Journal of the London Mathematical Society, vol. 21 (1946), pp. 167169.
[4] Kechris, A. S., Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, 1995.
[5] Ki, H. and Linton, T., Normal numbers and subsets ofwith given densities . Fundamenta Mathematicae, vol. 144 (1994), no. 2, pp. 163179.
[6] Kuipers, L. and Niederreiter, H., Uniform distribution of sequences, Wiley, New York, London, Sydney, 1974.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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