Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 77, Issue 2 (2012), 609-620.
RT₂² does not imply WKL₀
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.
J. Symbolic Logic, Volume 77, Issue 2 (2012), 609-620.
First available in Project Euclid: 4 April 2012
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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
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