Definable selector for $\bf\Delta^0_2$ sets modulo countable

TL;DR

This paper demonstrates that for every class of ^0_2 sets modulo countable, there exists an effective method to select a representative set.

Contribution

It introduces a definable selector function for ^0_2 sets modulo countable, advancing the understanding of effective selection in descriptive set theory.

Findings

Existence of an effective selector for ^0_2 sets modulo countable

Provides a definable method for choosing representatives in each class

Enhances the theory of effective descriptive set theory

Abstract

A set is effectively chosen in every class of $\bf\Delta^0_2$ sets modulo countable.