Canonizing certain Borel equivalences for Silver forcing

Following the recent research of J. Zapletal we study Borel equivalence relations with connection to the Silver forcing. We prove that ℓp relations and generally equivalence relations given by Fσ P-ideals can be canonized to the full equivalence relation or to a subset of E0. Next we classify a certain subclass of subequivalences of E0 on the Silver forcing and find perfectly many mutually different subequivalences of E0 with respect to the Silver forcing.