Geodesic
Normal numbers and the Borel hierarchy
Verónica Becher 1   ; Pablo Ariel Heiber 2   ; Theodore A. Slaman 3
1 Departamento de Computación Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires and CONICET Pabellón I, Ciudad Universitaria 1428 Buenos Aires, Argentina
2 Departamento de Computación Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires Pabellón I, Ciudad Universitaria 1428 Buenos Aires, Argentina
3 Department of Mathematics The University of California, Berkeley 719 Evans Hall #3840 Berkeley, CA 94720-3840, U.S.A.
Fundamenta Mathematicae, Tome 226 (2014) no. 1, pp. 63-77 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm226-1-4
Keywords: set absolutely normal numbers mathbf complete borel hierarchy subsets real numbers similarly set absolutely normal numbers complete effective borel hierarchy

Verónica Becher  1   ; Pablo Ariel Heiber  2   ; Theodore A. Slaman  3

1 Departamento de Computación Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires and CONICET Pabellón I, Ciudad Universitaria 1428 Buenos Aires, Argentina
2 Departamento de Computación Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires Pabellón I, Ciudad Universitaria 1428 Buenos Aires, Argentina
3 Department of Mathematics The University of California, Berkeley 719 Evans Hall #3840 Berkeley, CA 94720-3840, U.S.A. 
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Verónica Becher; Pablo Ariel Heiber; Theodore A. Slaman. Normal numbers and the Borel hierarchy. Fundamenta Mathematicae, Tome 226 (2014) no. 1, pp. 63-77. doi: 10.4064/fm226-1-4

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