On Borel ideals
In the main theorem it is shown that for every first category homogeneous Borel subspace of \({\mathcal P} (\omega)\) the following conditions are equivalent: (i) \(X\) can be embedded in \({\mathcal P} (\omega)\) as an ideal on \(\omega\); (ii) \(X\) is homeomorphic to \(X\times X\); (iii) \(X\) is Wadge- equivalent to \(X\times X\). Moreover, using the Wadge classes [cf. \textit{A. Louveau}, Cabal Semin. 79-81, Lect. Notes Math. 1019, 28-55 (1983; Zbl 0535.03026)] the author obtains a description of possible Wadge classes for Borel ideals on \(\omega\).
scientific article; zbMATH DE number 706879
scientific article