Open Access
2019 Π10-Encodability and Omniscient Reductions
Benoit Monin, Ludovic Patey
Notre Dame J. Formal Logic 60(1): 1-12 (2019). DOI: 10.1215/00294527-2018-0020


A set of integers A is computably encodable if every infinite set of integers has an infinite subset computing A. 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 Π10-encodable compact sets as those which admit a nonempty Σ11-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.


Download Citation

Benoit Monin. Ludovic Patey. "Π10-Encodability and Omniscient Reductions." Notre Dame J. Formal Logic 60 (1) 1 - 12, 2019.


Received: 3 March 2016; Accepted: 31 October 2016; Published: 2019
First available in Project Euclid: 18 January 2019

zbMATH: 07060305
MathSciNet: MR3911103
Digital Object Identifier: 10.1215/00294527-2018-0020

Primary: 03D30
Secondary: 03D65

Keywords: computable encodability , computable reduction , higher recursion theory , Ramsey’s theory , reverse mathematics

Rights: Copyright © 2019 University of Notre Dame

Vol.60 • No. 1 • 2019
Back to Top