Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 60, Number 1 (2019), 1-12.
-Encodability and Omniscient Reductions
Benoit Monin and Ludovic Patey
Abstract
A set of integers is computably encodable if every infinite set of integers has an infinite subset computing . By a result of Solovay, the computably encodable sets are exactly the hyperarithmetic ones. In this article, we extend this notion of computable encodability to subsets of the Baire space, and we characterize the -encodable compact sets as those which admit a nonempty -subset. Thanks to this equivalence, we prove that weak weak König’s lemma is not strongly computably reducible to Ramsey’s theorem. This answers a question of Hirschfeldt and Jockusch.
Article information
Source
Notre Dame J. Formal Logic, Volume 60, Number 1 (2019), 1-12.
Dates
Received: 3 March 2016
Accepted: 31 October 2016
First available in Project Euclid: 18 January 2019
Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1547802298
Digital Object Identifier
doi:10.1215/00294527-2018-0020
Mathematical Reviews number (MathSciNet)
MR3911103
Zentralblatt MATH identifier
07060305
Subjects
Primary: 03D30: Other degrees and reducibilities
Secondary: 03D65: Higher-type and set recursion theory
Keywords
reverse mathematics computable encodability Ramsey’s theory computable reduction higher recursion theory
Citation
Monin, Benoit; Patey, Ludovic. $\Pi ^{0}_{1}$ -Encodability and Omniscient Reductions. Notre Dame J. Formal Logic 60 (2019), no. 1, 1--12. doi:10.1215/00294527-2018-0020. https://projecteuclid.org/euclid.ndjfl/1547802298