The degree structure of Weihrauch-reducibility
Kojiro Higuchi (Tohoku University), Arno Pauly (University of, Cambridge)
TL;DR
This paper investigates the algebraic structure of Weihrauch degrees, demonstrating that the Weihrauch-lattice is not a Brouwer algebra but the continuous version is, and explores embeddings and lattice properties.
Contribution
It proves that the Weihrauch-lattice is not a Brouwer algebra and shows the continuous Weihrauch-lattice is a Heyting algebra, advancing understanding of its algebraic properties.
Findings
Weihrauch-lattice is not a Brouwer algebra
Continuous Weihrauch-lattice is a Heyting algebra
Analyzed embeddings of Medvedev-degrees into Weihrauch-degrees
Abstract
We answer a question by Vasco Brattka and Guido Gherardi by proving that the Weihrauch-lattice is not a Brouwer algebra. The computable Weihrauch-lattice is also not a Heyting algebra, but the continuous Weihrauch-lattice is. We further investigate the existence of infinite infima and suprema, as well as embeddings of the Medvedev-degrees into the Weihrauch-degrees.
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