Closed maximal eventually different families for ${\mathbf{\Sigma }}_3^0$ and weakly Farah ideals

Motivated by the existence of closed maximal $\mathcal{I}$-eventually different ($\mathcal{I}$-MED) families, we study uniform combinatorial properties of ideals. For a fixed ideal, a property is uniform if its witnesses can be chosen by a single Borel map. We prove that every ${\mathbf{\Sigma }}_3^0$ ideal is uniformly weakly $P^{+}$. We also prove that the classes of Farah and weakly Farah ideals coincide, answering a question of Hrušák and Meza-Alcántara. We then show that every weakly Farah ideal is uniformly weakly Ramsey. As an application, we obtain closed $\mathcal{I}$-MED families for ${\mathbf{\Sigma }}_3^0$ ideals and weakly Farah ideals.