Work

Investigating the Computable Friedman–stanley Jump

Year: 2023

Type: article

Abstract: The Friedman–Stanley jump, extensively studied by descriptive set theorists, is a fundamental tool for gauging the complexity of Borel isomorphism relations. This paper focuses on a natural computable analog of this jump operator for equivalence relations on $\omega $ , written ${\dotplus }$ , recently introduced by Clemens, Coskey, and Krakoff. We offer a thorough analysis of the computable Friedman–Stanley jump and its connections with the hierarchy of countable equivalence relations under the computable reducibility $\leq _c$ . In particular, we show that this jump gives benchmark equivalence relations going up the hyperarithmetic hierarchy and we unveil the complicated highness hierarchy that arises from ${\dotplus }$ .

Source: Journal of Symbolic Logic

DOI: 10.1017/jsl.2023.30

Authors: URI ANDREWS, LUCA SAN MAURO

Institutions: University of Wisconsin–Madison, TU Wien, Sapienza University of Rome

Language: English

Topic: Computability, Logic, AI Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,255

Funder: Austrian Science Fund