Abstract

Let E be a coanalytic equivalence relation on a Polish space X and (A n ) n∈ω a sequence of analytic subsets of X. We prove that if lim sup n∈K A n meets uncountably many E-equivalence classes for every K ∈ [ω] ω , then there exists a K ∈ [ω] ω such that ⋂ n∈K A n contains a perfect set of pairwise E-inequivalent elements