{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T10:17:50Z","timestamp":1777976270624,"version":"3.51.4"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2013,4,2]],"date-time":"2013-04-02T00:00:00Z","timestamp":1364860800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We answer a question by Vasco Brattka and Guido Gherardi by proving that the\nWeihrauch-lattice is not a Brouwer algebra. The computable Weihrauch-lattice is\nalso not a Heyting algebra, but the continuous Weihrauch-lattice is. We further\ninvestigate the existence of infinite infima and suprema, as well as embeddings\nof the Medvedev-degrees into the Weihrauch-degrees.<\/jats:p>","DOI":"10.2168\/lmcs-9(2:2)2013","type":"journal-article","created":{"date-parts":[[2013,11,29]],"date-time":"2013-11-29T13:39:25Z","timestamp":1385732365000},"source":"Crossref","is-referenced-by-count":20,"title":["The degree structure of Weihrauch-reducibility"],"prefix":"10.46298","volume":"Volume 9, Issue 2","author":[{"given":"Kojiro","family":"Higuchi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arno","family":"Pauly","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2013,4,2]]},"reference":[{"key":"750:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/lmcs.episciences.org\/1124\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/lmcs.episciences.org\/1124\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:04:11Z","timestamp":1681243451000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/lmcs.episciences.org\/1124"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,4,2]]},"references-count":1,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.2168\/lmcs-9(2:2)2013","relation":{"is-same-as":[{"id-type":"arxiv","id":"1101.0112","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1101.0112","asserted-by":"subject"}],"is-referenced-by":[{"id-type":"arxiv","id":"1501.00433","asserted-by":"subject"},{"id-type":"doi","id":"10.1007\/s00224-017-9798-1","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arxiv.1501.00433","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,4,2]]},"article-number":"1124"}}