The weakness of finding descending sequences in ill-founded linear orders

Jun Le Goh, Arno Pauly, Manlio Valenti

Published 2024-01-22Version 1

We prove that the Weihrauch degree of the problem of finding a bad sequence in a non-well quasi order ($\mathsf{BS}$) is strictly above that of finding a descending sequence in an ill-founded linear order ($\mathsf{DS}$). This corrects our mistaken claim in arXiv:2010.03840, which stated that they are Weihrauch equivalent. We prove that K\"onig's lemma $\mathsf{KL}$ is not Weihrauch reducible to $\mathsf{DS}$ either, resolving the main open question raised in arXiv:2010.03840.