Singular sets and Baire order (Q1067245)

The property of subsets X of reals to have countable Baire order (i.e. the procedure of forming \(G_{\delta}\)-sets, \(G_{\delta \sigma}\)-sets, etc. in X stops at a countable ordinal) is included into a diagram of implications between other singular properties of subsets of reals. It is stated that every set having countable Baire order is an \((S)_ 0\)-set. Several open questions are posed.