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arXiv · 1610.00878

Reverse mathematics of the finite downwards closed subsets of $\mathbb{N}^k$ ordered by inclusion and adjacent Ramsey for fixed dimension

Florian Pelupessy
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Abstract

We show that the well-partial orderedness of the finite downwards closed subsets of $\mathbb{N}^k$ ,ordered by inclusion, is equivalent to the well-foundedness of the ordinal $ω^{ω^ω}$. This was conjectured to be the case by Hatzikiriakou and Simpson. Since we use Friedman's adjacent Ramsey theorem for fixed dimensions in the upper bound, we also give a treatment of the reverse mathematical status of that theorem.

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Florian Pelupessy. 2017-10-04. Reverse mathematics of the finite downwards closed subsets of $\mathbb{N}^k$ ordered by inclusion and adjacent Ramsey for fixed dimension. https://doi.org/10.1002/malq.201700040

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