{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T01:09:19Z","timestamp":1782263359173,"version":"3.54.5"},"reference-count":20,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":8685,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1990,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper investigates the algebraic structure of the Medvedev lattice <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200026189_inline1\"\/>. We prove that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200026189_inline1\"\/> is not a Heyting algebra. We point out some relations between <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200026189_inline1\"\/> and the Dyment lattice and the Mu\u010dnik lattice. Some properties of the degrees of enumerability are considered. We give also a result on embedding countable distributive lattices in the Medvedev lattice.<\/jats:p>","DOI":"10.2307\/2274668","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:35:29Z","timestamp":1146954929000},"page":"831-853","source":"Crossref","is-referenced-by-count":18,"title":["Some remarks on the algebraic structure of the Medvedev Lattice"],"prefix":"10.1017","volume":"55","author":[{"given":"Andrea","family":"Sorbi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200026189_ref019","unstructured":"Sorbi A. , The fine structure of the Medvedev lattice and the partial degrees, Ph.D. thesis, Graduate Center, City University of New York, New York, 1987."},{"key":"S0022481200026189_ref017","unstructured":"Sorbi A. , On some filters and ideals of the Medvedev lattice (to appear)."},{"key":"S0022481200026189_ref013","volume-title":"Theory of recursive functions and effective computability","author":"Rogers","year":"1967"},{"key":"S0022481200026189_ref011","first-page":"1328","article-title":"On strong and weak reducibility of algorithmic problems","volume":"4","author":"Mu\u010dnik","year":"1963","journal-title":"Sibirski\u012d Matemati\u010deski\u012d \u017durnal"},{"key":"S0022481200026189_ref010","first-page":"501","article-title":"Degrees of difficulty of the mass problems","volume":"104","author":"Medvedev","year":"1955","journal-title":"Doklady Akademii Nauk SSSR"},{"key":"S0022481200026189_ref008","first-page":"303","article-title":"Modal diagonalizable algebras","volume":"15","author":"Magari","year":"1978","journal-title":"Bollettino dell'Unione Matematica Italiana B"},{"key":"S0022481200026189_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF02761906"},{"key":"S0022481200026189_ref001","volume-title":"Distributive lattices","author":"Balbes","year":"1974"},{"key":"S0022481200026189_ref005","first-page":"899","article-title":"Exact bounds of denumerable collections of degrees of difficulty","volume":"28","author":"Dyment","year":"1980","journal-title":"Matemati\u010deskie Zametki"},{"key":"S0022481200026189_ref004","first-page":"360","article-title":"Certain properties of the Medvedev lattice","volume":"101","author":"Dyment","year":"1976","journal-title":"Matemati\u010deski\u012d Sbornik"},{"key":"S0022481200026189_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21755-9"},{"key":"S0022481200026189_ref014","first-page":"71","volume-title":"Recursive functions","author":"Rozinas","year":"1978"},{"key":"S0022481200026189_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/BF02123402"},{"key":"S0022481200026189_ref002","first-page":"854","volume":"47","author":"Cooper","year":"1982","journal-title":"Partial degrees and the density problem"},{"key":"S0022481200026189_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9839-7"},{"key":"S0022481200026189_ref020","doi-asserted-by":"publisher","DOI":"10.1007\/BF02488034"},{"key":"S0022481200026189_ref016","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"},{"key":"S0022481200026189_ref012","first-page":"917","article-title":"A note on the cardinality of the Medvedev lattice","volume":"25","author":"Platek","year":"1970","journal-title":"Proceedings of the American Mathematical Society"},{"key":"S0022481200026189_ref018","unstructured":"Sorbi A. , Embedding Brouwer algebras in the Medvedev lattice (to appear)."},{"key":"S0022481200026189_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/S1385-7258(66)50036-1"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200026189","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T21:13:44Z","timestamp":1558214024000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200026189\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,6]]},"references-count":20,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1990,6]]}},"alternative-id":["S0022481200026189"],"URL":"https:\/\/doi.org\/10.2307\/2274668","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,6]]}}}