Title: Joins in the strong Weihrauch degrees,
Abstract: The Weihrauch degrees and strong Weihrauch degrees are partially ordered
structures representing degrees of unsolvability of various mathematical
problems. Their study has been widely applied in computable analysis,
complexity theory, and more recently, also in computable combinatorics. We
answer an open question about the algebraic structure of the strong Weihrauch
degrees, by exhibiting a join operation that turns these degrees into a
lattice. Previously, the strong Weihrauch degrees were only known to form a
lower semi-lattice. We then show that unlike the Weihrauch degrees, which are
known to form a distributive lattice, the lattice of strong Weihrauch degrees
is not distributive. Therefore, the two structures are not isomorphic.