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  1. Measure theory and weak König's lemma.Xiaokang Yu & Stephen G. Simpson - 1990 - Archive for Mathematical Logic 30 (3):171-180.
    We develop measure theory in the context of subsystems of second order arithmetic with restricted induction. We introduce a combinatorial principleWWKL (weak-weak König's lemma) and prove that it is strictly weaker thanWKL (weak König's lemma). We show thatWWKL is equivalent to a formal version of the statement that Lebesgue measure is countably additive on open sets. We also show thatWWKL is equivalent to a formal version of the statement that any Borel measure on a compact metric space is countably additive (...)
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  • RT2 2 does not imply WKL0.Jiayi Liu - 2012 - Journal of Symbolic Logic 77 (2):609-620.
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  • RT₂² does not imply WKL₀.Jiayi Liu - 2012 - Journal of Symbolic Logic 77 (2):609-620.
    We prove that RCA₀ + RT $RT\begin{array}{*{20}{c}} 2 \\ 2 \\ \end{array} $ ̸͢ 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 ̅Α, such that G ⊕ C is also not of PA-degree.
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  • Separating principles below Ramsey's theorem for pairs.Manuel Lerman, Reed Solomon & Henry Towsner - 2013 - Journal of Mathematical Logic 13 (2):1350007.
    In recent years, there has been a substantial amount of work in reverse mathematics concerning natural mathematical principles that are provable from RT, Ramsey's Theorem for Pairs. These principles tend to fall outside of the "big five" systems of reverse mathematics and a complicated picture of subsystems below RT has emerged. In this paper, we answer two open questions concerning these subsystems, specifically that ADS is not equivalent to CAC and that EM is not equivalent to RT.
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  • Reverse mathematics and a Ramsey-type König's Lemma.Stephen Flood - 2012 - Journal of Symbolic Logic 77 (4):1272-1280.
    In this paper, we propose a weak regularity principle which is similar to both weak König's lemma and Ramsey's theorem. We begin by studying the computational strength of this principle in the context of reverse mathematics. We then analyze different ways of generalizing this principle.
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  • Comparing DNR and WWKL.Klaus Ambos-Spies, Bjørn Kjos-Hanssen, Steffen Lempp & Theodore A. Slaman - 2004 - Journal of Symbolic Logic 69 (4):1089-1104.
    In Reverse Mathematics, the axiom system DNR, asserting the existence of diagonally non-recursive functions, is strictly weaker than WWKL0.
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