Construction of Borel inseparable coanalytic sets.

Abstract

We prove general results from which large families of pairwise disjoint, Borel inseparable, complete coanalytic sets can be obtained. The elements of such families are naturally indexed by $2^{\aleph _0}$, $\omega _1$ or the classes of a Borel complete equivalence relation. We also give some concrete examples of such families in analysis, topology etc.