Weihrauch degrees without roots

08/01/2023

∙

by   Patrick Uftring, et al.

∙

0

∙

share

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.