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arXiv · 1101.0112

The degree structure of Weihrauch-reducibility

Kojiro Higuchi·Arno Pauly
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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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Kojiro Higuchi, Arno Pauly. 2013-04-01. The degree structure of Weihrauch-reducibility. https://doi.org/10.2168/lmcs-9(2%3A2)2013

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