Abstract
We prove that RCA₀+RT₂² ⇸ WKL₀ by showing that for any set C not of PA-degree and any set A, there exists an infinite subset G of A or A̅, such that G⊕C is also not of PA-degree.
Citation
Jiayi Liu. "RT₂² does not imply WKL₀." J. Symbolic Logic 77 (2) 609 - 620, June 2012. https://doi.org/10.2178/jsl/1333566640
Information
Published: June 2012
First available in Project Euclid: 4 April 2012
MathSciNet: MR2963024
Digital Object Identifier: 10.2178/jsl/1333566640
Subjects:
Primary:
03C62
,
03D30
,
03D80
,
03F35
Keywords:
computability theory
,
Mathias forcing
,
Ramsey's theorem
,
recursion theory
,
reverse mathematics
,
weak Konig lemma
Rights: Copyright © 2012 Association for Symbolic Logic
