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- Title
INVESTIGATING THE COMPUTABLE FRIEDMAN–STANLEY JUMP.
- Authors
ANDREWS, URI; SAN MAURO, LUCA
- 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 ${\dotplus }$.
- Subjects
GAGING; THEORISTS; GAGES
- Publication
Journal of Symbolic Logic, 2024, Vol 89, Issue 2, p918
- ISSN
0022-4812
- Publication type
Article
- DOI
10.1017/jsl.2023.30