Reverse mathematics of the finite downwards closed subsets of $\mathbb{N}^k$ ordered by inclusion

Florian Pelupessy

Published 2016-10-04Version 1

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 $\omega^{\omega^\omega}$. This was conjectured to be so by Hatzikiriakou and Simpson.