{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T10:07:43Z","timestamp":1775642863572,"version":"3.50.1"},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":6676,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1995,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that the \u03a0<jats:sub>4<\/jats:sub>-theory of the partial order of recursively enumerable weak truth-table degrees is undecidable, and give a new proof of the similar fact for r.e. T-degrees. This is accomplished by introducing a new coding scheme which consists in defining the class of finite bipartite graphs with parameters.<\/jats:p>","DOI":"10.2307\/2275877","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:56:55Z","timestamp":1146956215000},"page":"1118-1136","source":"Crossref","is-referenced-by-count":8,"title":["The undecidability of the \u03a0<sub>4<\/sub>-theory for the r.e. wtt and Turing degrees"],"prefix":"10.1017","volume":"60","author":[{"given":"Steffen","family":"Lempp","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andr\u00e9","family":"Nies","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200017953_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1982-14970-9"},{"key":"S0022481200017953_ref011","unstructured":"Nies A. , Definability and undecidability in recursion theoretic semi-lattices, Ph.D. thesis, Universit\u00e4t Heidelberg, Heidelberg, 1992."},{"key":"S0022481200017953_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)90206-S"},{"key":"S0022481200017953_ref012","volume-title":"Algebra Universalis","author":"Nies"},{"key":"S0022481200017953_ref003","first-page":"864","volume":"57","author":"Ambos-Spies","year":"1992","journal-title":"The theory of the r.e. weak truth-table degrees is undecidable"},{"key":"S0022481200017953_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(75)90007-8"},{"key":"S0022481200017953_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF02218612"},{"key":"S0022481200017953_ref007","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-16.1.537"},{"key":"S0022481200017953_ref006","first-page":"987","volume":"55","author":"Haught","year":"1990","journal-title":"Undecidability and initial segments of the {r.e.) tt-degrees"},{"key":"S0022481200017953_ref002","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19850312903"},{"key":"S0022481200017953_ref001","first-page":"58","volume-title":"Computation and proof theory (Proceedings of Logic Colloquium '83, Aachen)","volume":"1104","author":"Ambos-Spies","year":"1984"},{"key":"S0022481200017953_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21755-9"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200017953","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T20:18:35Z","timestamp":1557778715000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200017953\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,12]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1995,12]]}},"alternative-id":["S0022481200017953"],"URL":"https:\/\/doi.org\/10.2307\/2275877","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,12]]}}}