Constructive Combinatorics of Dickson's Lemma
Combinatorics
2022-04-26 v1
Abstract
We study constructively the relations between the finite cases of Dickson's lemma. Although there are many constructive proofs of them, the novel aspect of our proofs is the extraction of a corresponding bound. We provide some new one-step unprovability results i.e., results of the form "a finite case of Dickson's lemma does not prove in one step a stronger case of it". Moreover, we study the infinite cases of Dickson's lemma from the point of view of constructive reverse mathematics. We work within Bishop's informal system of constructive mathematics BISH.
Keywords
Cite
@article{arxiv.2204.11298,
title = {Constructive Combinatorics of Dickson's Lemma},
author = {Iosif Petrakis},
journal= {arXiv preprint arXiv:2204.11298},
year = {2022}
}