English

Weihrauch degrees without roots

Logic 2023-08-07 v1 Logic in Computer Science

Abstract

We answer the following question by Arno Pauly: "Is there a square-root operator on the Weihrauch degrees?". In fact, we show that there are uncountably many pairwise incomparable Weihrauch degrees without any roots. We also prove that the omniscience principles of LPO and LLPO do not have roots.

Cite

@article{arxiv.2308.01422,
  title  = {Weihrauch degrees without roots},
  author = {Patrick Uftring},
  journal= {arXiv preprint arXiv:2308.01422},
  year   = {2023}
}
R2 v1 2026-06-28T11:46:50.198Z