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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
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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.

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 

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References

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