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 $\mathsf{KL}$ and the problem $\mathsf{wList}_{2^{\mathbb{N}},\leq\omega}$ of enumerating a given non-empty countable closed subset of $2^\mathbb{N}$ are not Weihrauch reducible to $\mathsf{DS}$ either, resolving two main open questions raised in arXiv:2010.03840.
翻译:我们证明了在非良拟序中寻找坏序列问题($\mathsf{BS}$)的Weihrauch度严格高于在非良基线性序中寻找降序列问题($\mathsf{DS}$)的Weihrauch度。这纠正了我们先前在arXiv:2010.03840中的错误主张,该主张声称它们是Weihrauch等价的。我们还证明了K\"onig引理$\mathsf{KL}$以及枚举给定非空可数闭子集问题$\mathsf{wList}_{2^{\mathbb{N}},\leq\omega}$均不能Weihrauch归约到$\mathsf{DS}$,从而解决了arXiv:2010.03840中提出的两个主要开放性问题。