Geodesic
Normal numbers and the Borel hierarchy
Verónica Becher1 ; Pablo Ariel Heiber2 ; Theodore A. Slaman3
1Departamento de Computación Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires and CONICET Pabellón I, Ciudad Universitaria 1428 Buenos Aires, Argentina
2Departamento de Computación Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires Pabellón I, Ciudad Universitaria 1428 Buenos Aires, Argentina
3Department 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

Voir la notice de l'article

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. 
@article{10_4064_fm226_1_4,
     author = {Ver\'onica Becher and Pablo Ariel Heiber and Theodore A. Slaman},
     title = {Normal numbers and the {Borel} hierarchy},
     journal = {Fundamenta Mathematicae},
     pages = {63--77},
     year = {2014},
     volume = {226},
     number = {1},
     doi = {10.4064/fm226-1-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm226-1-4/}
}
TY  - JOUR
AU  - Verónica Becher
AU  - Pablo Ariel Heiber
AU  - Theodore A. Slaman
TI  - Normal numbers and the Borel hierarchy
JO  - Fundamenta Mathematicae
PY  - 2014
SP  - 63
EP  - 77
VL  - 226
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm226-1-4/
DO  - 10.4064/fm226-1-4
LA  - en
ID  - 10_4064_fm226_1_4
ER  - 
%0 Journal Article
%A Verónica Becher
%A Pablo Ariel Heiber
%A Theodore A. Slaman
%T Normal numbers and the Borel hierarchy
%J Fundamenta Mathematicae
%D 2014
%P 63-77
%V 226
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/fm226-1-4/
%R 10.4064/fm226-1-4
%G en
%F 10_4064_fm226_1_4
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

Cité par Sources :