Measure-theoretic Uniformity and the Suslin Functional

TL;DR

This paper extends measure-theoretic uniformity results and basis theorems from hyperarithmetical sets to computability relative to the Suslin functional, connecting classical descriptive set theory with higher computability theory.

Contribution

It generalizes classical measure-theoretic uniformity and basis results to the setting of the Suslin functional and hyperjump, bridging descriptive set theory and computability theory.

Findings

Extended measure-theoretic uniformity to Suslin functional

Proved basis theorem for $\Pi^1_1$-sets of positive measure

Connected classical results with higher computability concepts

Abstract

We generalise results by Sacks and Tanaka concerning measure-theoretic uniformity for hyperarithmetical sets and a basis theorem for $\Pi^1_1$-sets of positive measure to computability and semicomputability relative to the Suslin functional, alternatively to the (equivalent) Hyperjump.