2000 character limit reached
The Dyck and the Preiss separation uniformly (1703.06480v1)
Published 19 Mar 2017 in math.LO
Abstract: We are concerned with two separation theorems about analytic sets by Dyck and Preiss, the former involves the positively-defined subsets of the Cantor space and the latter the Borel-convex subsets of finite dimensional Banach spaces. We show by introducing the corresponding separation trees that both of these results admit a constructive proof. This enables us to give the uniform version of the separation theorems, and derive as corollaries the results, which are analogous to the fundamental fact "HYP is effectively bi-analytic" provided by the Souslin-Kleene Theorem.