# How to recognize a true Σ^0_3 set

Fundamenta Mathematicae (1998)

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

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topMatheron, 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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