Reverse mathematics of the finite downwards closed subsets of ordered by inclusion and adjacent Ramsey for fixed dimension
Florian Pelupessy · Mathematical logic quarterly · 2018
Abstract We show that the well partial orderedness of the finite downwards closed subsets of , ordered by inclusion, is equivalent to the well foundedness of the ordinal . 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.