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Normal numbers and the Borel hierarchy

Volume 226 / 2014

Verónica Becher, Pablo Ariel Heiber, Theodore A. Slaman Fundamenta Mathematicae 226 (2014), 63-77 MSC: 11U99, 03E15, 68W99. DOI: 10.4064/fm226-1-4

Abstract

We show that the set of absolutely normal numbers is $\mathbf \Pi ^0_3$-complete in the Borel hierarchy of subsets of real numbers. Similarly, the set of absolutely normal numbers is $\Pi ^0_3$-complete in the effective Borel hierarchy.

Authors

  • Verónica BecherDepartamento de Computación
    Facultad de Ciencias Exactas y Naturales
    Universidad de Buenos Aires
    and
    CONICET
    Pabellón I, Ciudad Universitaria
    1428 Buenos Aires, Argentina
    e-mail
  • Pablo Ariel HeiberDepartamento de Computación
    Facultad de Ciencias Exactas y Naturales
    Universidad de Buenos Aires
    Pabellón I, Ciudad Universitaria
    1428 Buenos Aires, Argentina
    e-mail
  • Theodore A. SlamanDepartment of Mathematics
    The University of California, Berkeley
    719 Evans Hall #3840
    Berkeley, CA 94720-3840, U.S.A.
    e-mail

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