How to recognize a true $Σ^0_3$ set
Volume 158 / 1998
Fundamenta Mathematicae 158 (1998), 181-194
DOI: 10.4064/fm-158-2-181-194
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 $∑_3^0$.
