Normal numbers and subsets of N with given densities

@inproceedings{MATHEMATICAE2007NormalNA,
  title={Normal numbers and subsets of N with given densities},
  author={FUNDAMENTA MATHEMATICAE},
  year={2007}
}
  • FUNDAMENTA MATHEMATICAE
  • Published 2007
For X ⊆ [0, 1], let DX denote the collection of subsets of N whose densities lie in X. Given the exact location of X in the Borel or difference hierarchy, we exhibit the exact location of DX . For α ≥ 3, X is properly Dξ(Π α) iff DX is properly Dξ(Π 1+α). We also show that for every nonempty set X ⊆ [0, 1], DX is Π0 3 -hard. For each nonempty Π0 2 set X ⊆ [0, 1], in particular for X = {x}, DX is Π0 3 -complete. For each n ≥ 2, the collection of real numbers that are normal or simply normal to… CONTINUE READING
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References

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Showing 1-4 of 4 references

Irrational Numbers, The Carus Math

  • I. Niven
  • 1956
Highly Influential
3 Excerpts

Louveau and J . Sa intRaymond , Borel classes and closed games : Wadgetype and Hurewicztype results

  • A.
  • Trans . Amer . Math . Soc .
  • 1974

Degrees of complexity of subsets of the Baire space

  • W. Wadge
  • Notices Amer. Math. Soc
  • 1972
1 Excerpt

On normal numbers, Pacific

  • W. Schmidt
  • J. Math
  • 1960
1 Excerpt

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