Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-02-06T05:05:21.959Z Has data issue: false hasContentIssue false
  • English
  • Français

NORMAL NUMBERS AND COMPLETENESS RESULTS FOR DIFFERENCE SETS

Published online by Cambridge University Press:  21 March 2017

KONSTANTINOS A. BEROS
KONSTANTINOS A. BEROS*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF NORTH TEXAS GENERAL ACADEMICS BUILDING 435 1155 UNION CIRCLE, #311430, DENTON TX 76203-5017, USAE-mail: beros@unt.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

03E1528A05difference hierarchynormal numberscompleteness
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 1 , March 2017 , pp. 247 - 257
Copyright
Copyright © The Association for Symbolic Logic 2017 

References

REFERENCES

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. 472–494.CrossRefGoogle Scholar
Becher, V., Ariel Heiber, P. and Slaman, T., Normal numbers in the Borel hierarchy . Fundamenta Mathematicae, vol. 226 (2014), pp. 63–77.CrossRefGoogle Scholar
Good, I. J., Normal recurring decimals . Journal of the London Mathematical Society, vol. 21 (1946), pp. 167–169.CrossRefGoogle Scholar
Kechris, A. S., Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, 1995.CrossRefGoogle Scholar
Ki, H. and Linton, T., Normal numbers and subsets of ℕ with given densities . Fundamenta Mathematicae, vol. 144 (1994), no. 2, pp. 163–179.CrossRefGoogle Scholar
Kuipers, L. and Niederreiter, H., Uniform distribution of sequences, Wiley, New York, London, Sydney, 1974.Google Scholar