  Let A and B be subsets of the plane (ωω)2. A uniformizes B iff A ⊆ B and for all x ∈ ωω, there exists y such that ⟨x,y⟩ ∈ B iff there is a unique y such that ⟨x,y⟩ ∈ A. In other words, A yields a choice function for B. Using AC it is clear that every set B has a uniformizing set A. However, the question of whether uniformizations exist becomes interesting when one imposes a definability constraint. Let Γ be a collection of (k-tuples of) sets of reals. Such a class is called a pointclass. The pointclass Γ has uniformization property (Unif(Γ)) iff every subset of the plane that is in Γ admits a uniformization that is also in Γ. 