How to recognize a true Σ^0_3 set

Etienne Matheron

Fundamenta Mathematicae (1998)

  • Volume: 158, Issue: 2, page 181-194
  • ISSN: 0016-2736

Abstract

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Let X be a Polish space, and let ( A p ) p ∈ ω be a sequence of G δ hereditary subsets of K(X) (the space of compact subsets of X). We give a general criterion which allows one to decide whether ∪ p ∈ ω A p is a true ∑ 3 0 subset of K(X). We apply this criterion to show that several natural families of thin sets from harmonic analysis are true ∑ 3 0 .

How to cite

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Matheron, Etienne. "How to recognize a true Σ^0_3 set." Fundamenta Mathematicae 158.2 (1998): 181-194. <http://eudml.org/doc/212310>.

@article{Matheron1998,
abstract = {Let X be a Polish space, and let $(A_p)_\{p∈ω\}$ be a sequence of $G_δ$ hereditary subsets of K(X) (the space of compact subsets of X). We give a general criterion which allows one to decide whether $∪_\{p∈ω\}A _p$ is a true $∑_3^0$ subset of K(X). We apply this criterion to show that several natural families of thin sets from harmonic analysis are true $∑_3^0$.},
author = {Matheron, Etienne},
journal = {Fundamenta Mathematicae},
keywords = {true set; ideal of ; Polish space; ideal of compact sets},
language = {eng},
number = {2},
pages = {181-194},
title = {How to recognize a true Σ^0\_3 set},
url = {http://eudml.org/doc/212310},
volume = {158},
year = {1998},
}

TY - JOUR
AU - Matheron, Etienne
TI - How to recognize a true Σ^0_3 set
JO - Fundamenta Mathematicae
PY - 1998
VL - 158
IS - 2
SP - 181
EP - 194
AB - Let X be a Polish space, and let $(A_p)_{p∈ω}$ be a sequence of $G_δ$ hereditary subsets of K(X) (the space of compact subsets of X). We give a general criterion which allows one to decide whether $∪_{p∈ω}A _p$ is a true $∑_3^0$ subset of K(X). We apply this criterion to show that several natural families of thin sets from harmonic analysis are true $∑_3^0$.
LA - eng
KW - true set; ideal of ; Polish space; ideal of compact sets
UR - http://eudml.org/doc/212310
ER -

References

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  1. [GMG] C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Grundlehren Math. Wiss. 238, Springer, New York, 1979. 
  2. [G] M. B. Gregory, p-Helson sets, 1 < p < 2, Israel J. Math. 12 (1972), 356-368. 
  3. [Ke1] A. S. Kechris, Hereditary properties of the class of closed sets of uniqueness for trigonometric series, ibid. 73 (1991), 189-198. 
  4. [Ke2] A. S. Kechris, Classical Descriptive Set Theory, Springer, New York, 1995. 
  5. [KL] A. S. Kechris and A. Louveau, Descriptive Set Theory and the Structure of Sets of Uniqueness, London Math. Soc. Lecture Note Ser. 128, Cambridge Univ. Press, 1987. Zbl0642.42014
  6. [LP] L.-A. Lindahl and A. Poulsen, Thin Sets in Harmonic Analysis, Marcel Dekker, New York, 1971. 
  7. [Li] T. Linton, The H-sets of the unit circle are properly G δ σ , Real Anal. Exchange 19 (1994), 203-211. 
  8. [Ly] R. Lyons, A new type of sets of uniqueness, Duke Math. J. 57 (1988), 431-458. Zbl0677.42006
  9. [M] E. Matheron, The descriptive complexity of Helson sets, Illinois J. Math. 39 (1995), 608-625. Zbl0843.43004
  10. [T] V. Tardivel, Fermés d'unicité dans les groupes abéliens localement compacts, Studia Math. 91 (1988), 1-15. Zbl0666.43002

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