The degree structure of Weihrauch-reducibility

Kojiro Higuchi, Arno Pauly, S. Barry Cooper
2013 Logical Methods in Computer Science  
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.
doi:10.2168/lmcs-9(2:2)2013 fatcat:gy4ole5nffgbjbfhzrn5luzai4