We study the existence and the distribution of “long” chains in the Weihrauch degrees, mostly focusing on chains with uncountable cofinality. We characterize when such chains have an upper bound and prove that there are no cofinal chains (of any order type) in the Weihrauch degrees. Furthermore, we show that the existence of coinitial sequences of non-zero degrees is equivalent to CH. Finally, we explore the extendibility of antichains, providing some necessary conditions for maximality.
CHAINS AND ANTICHAINS IN THE WEIHRAUCH LATTICE
Marcone A.;
2026-01-01
Abstract
We study the existence and the distribution of “long” chains in the Weihrauch degrees, mostly focusing on chains with uncountable cofinality. We characterize when such chains have an upper bound and prove that there are no cofinal chains (of any order type) in the Weihrauch degrees. Furthermore, we show that the existence of coinitial sequences of non-zero degrees is equivalent to CH. Finally, we explore the extendibility of antichains, providing some necessary conditions for maximality.File in questo prodotto:
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