How to recognize a true Σ^0_3 set
Etienne Matheron (1998)
Fundamenta Mathematicae
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Let X be a Polish space, and let be a sequence of hereditary subsets of K(X) (the space of compact subsets of X). We give a general criterion which allows one to decide whether is a true subset of K(X). We apply this criterion to show that several natural families of thin sets from harmonic analysis are true .