Journal of Symbolic Logic

RT₂² does not imply WKL₀

Jiayi Liu

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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.

Article information

Source
J. Symbolic Logic, Volume 77, Issue 2 (2012), 609-620.

Dates
First available in Project Euclid: 4 April 2012

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1333566640

Digital Object Identifier
doi:10.2178/jsl/1333566640

Mathematical Reviews number (MathSciNet)
MR2963024

Subjects
Primary: 03F35: Second- and higher-order arithmetic and fragments [See also 03B30] 03C62: Models of arithmetic and set theory [See also 03Hxx] 03D30: Other degrees and reducibilities 03D80: Applications of computability and recursion theory

Keywords
recursion theory computability theory reverse mathematics Ramsey's theorem weak Konig lemma Mathias forcing

Citation

Liu, Jiayi. RT₂² does not imply WKL₀. J. Symbolic Logic 77 (2012), no. 2, 609--620. doi:10.2178/jsl/1333566640. https://projecteuclid.org/euclid.jsl/1333566640


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