Abstract
We prove that Higman’s lemma is strictly stronger for better quasi orders than for well quasi orders, within the framework of reverse mathematics. In fact, we show a stronger result: the infinite Ramsey theorem (for tuples of all lengths) is equivalent to the statement that any array \([\mathbb N]^{n+1}\rightarrow \mathbb N^n\times X\) for a well order X and \(n\in \mathbb N\) is good, over the base theory \(\mathsf {RCA_0}\).
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Open Access funding enabled and organized by Projekt DEAL. The author’s work has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project number 460597863.
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Freund, A. Higman’s Lemma is Stronger for Better Quasi Orders. Order (2024). https://doi.org/10.1007/s11083-024-09658-w
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DOI: https://doi.org/10.1007/s11083-024-09658-w