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• W3135855384 abstract "Let $mathsf {TT}^2_k$ denote the combinatorial principle stating that every $k$-coloring of pairs of compatible nodes in the full binary tree has a homogeneous solution, i.e. an isomorphic subtree in which all pairs of compatible nodes have the same color. Let $mathsf {WKL}_0$ be the subsystem of second order arithmetic consisting of the base system $mathsf {RCA}_0$ together with the principle (called Weak König’s Lemma) stating that every infinite subtree of the full binary tree has an infinite path. We show that over $mathsf {RCA}_0$, $mathsf {TT}^2_k$ does not imply $mathsf {WKL}_0$. This solves the open problem on the relative strength between the two major subsystems in second order arithmetic." @default.
• W3135855384 created "2021-03-15" @default.
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• W3135855384 date "2021-05-20" @default.
• W3135855384 modified "2023-10-17" @default.
• W3135855384 title "The strength of Ramsey’s theorem for pairs over trees: I. Weak König’s Lemma" @default.
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• W3135855384 doi "https://doi.org/10.1090/tran/8339" @default.
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