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INVESTIGATING THE COMPUTABLE FRIEDMAN–STANLEY JUMP.
- Source :
- Journal of Symbolic Logic; Jun2024, Vol. 89 Issue 2, p918-944, 27p
- Publication Year :
- 2024
-
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 ${\dotplus }$. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00224812
- Volume :
- 89
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Journal of Symbolic Logic
- Publication Type :
- Academic Journal
- Accession number :
- 177377050
- Full Text :
- https://doi.org/10.1017/jsl.2023.30