Abstract Assume $\mathsf {ZF} + \mathsf {AD}$ and all sets of reals are Suslin. Let $\Gamma $ be a pointclass closed under $\wedge $ , $\vee $ , $\forall ^{\mathbb {R}}$ , continuous substitution, and has the scale property. Let $\kappa = \delta (\Gamma )$ be the supremum of the length of prewellorderings on $\mathbb {R}$ which belong to $\Delta = \Gamma \cap \check \Gamma $ . Let $\mathsf {club}$ denote the collection of club subsets of $\kappa $ . Then the countable length everywhere club uniformization holds for $\kappa $ : For every relation $R \subseteq {}^{<{\omega _1}}\kappa \times \mathsf {club}$ with the property that for all $\ell \in {}^{<{\omega _1}}\kappa $ and clubs $C \subseteq D \subseteq \kappa $ , $R(\ell ,D)$ implies $R(\ell ,C)$ , there is a uniformization function $\Lambda : \mathrm {dom}(R) \rightarrow \mathsf {club}$ with the property that for all $\ell \in \mathrm {dom}(R)$ , $R(\ell ,\Lambda (\ell ))$ . In particular, under these assumptions, for all $n \in \omega $ , $\boldsymbol {\delta }^1_{2n + 1}$ satisfies the countable length everywhere club uniformization.

Abstract The following will be shown: Let I be a σ-ideal on a Polish space X so that the associated forcing of I+ ${\bf{\Delta }}_1^1$ sets ordered by ⊆ is a proper forcing. Let E be a ${\bf{\Sigma }}_1^1$ or a ${\bf{\Pi }}_1^1$ equivalence relation on X with all equivalence classes ${\bf{\Delta }}_1^1$ . If for all $z \in {H_{{{\left( {{2^{{\aleph _0}}}} \right)}^ + }}}$ , z♯ exists, then there exists an I+ ${\bf{\Delta }}_1^1$ set C ⊆ X such that E ↾ C is a ${\bf{\Delta }}_1^1$ equivalence relation.