Investigating the computable Friedman-Stanley jump

TL;DR

This paper explores the computable Friedman-Stanley jump on equivalence relations, linking computable reduction theory with descriptive set theory to deepen understanding of their relationship.

Contribution

It provides new insights into the properties of the computable Friedman-Stanley jump and its connection to Borel reducibility.

Findings

Analyzed the properties of the computable Friedman-Stanley jump.

Established connections between computable and Borel reducibility.

Answered key questions about the jump's behavior and implications.

Abstract

We answer several questions about the computable Friedman-Stanley jump on equivalence relations. This jump, introduced by Clemens, Coskey, and Krakoff, deepens the natural connection between the study of computable reduction and its Borel analog studied deeply in descriptive set theory.