On the characterization of Souslin and Borel sets

Abstract:

Let $\mathfrak {X}$ be an arbitrary family of sets in the basic set $X$. In this paper Souslin-$\mathfrak {X}$ sets are represented as projections on $X$ of certain $\sigma \delta$-sets in the cartesian product space of $X$ and the Baire space (or $X$ and the real line). For $L{\text { - }}\mathfrak {X}$ sets (i.e. Souslin sets defined with disjoint unions; ensembles d’unicité) injective projections are considered. The results also apply to Borel-$\mathfrak {X}$ sets since the system of $L{\text { - }}\mathfrak {X}$ sets includes the Borel-$\mathfrak {X}$ sets under suitable conditions.