{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T15:55:55Z","timestamp":1648569355747},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":7132,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1994,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We settle a question in the literature about degrees of models of true arithmetic and upper bounds for the arithmetic sets. We prove that there is a model of true arithmetic whose degree is not a uniform upper bound for the arithmetic sets. The proof involves two forcing constructions.<\/jats:p>","DOI":"10.2307\/2275921","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:52:43Z","timestamp":1146955963000},"page":"977-983","source":"Crossref","is-referenced-by-count":5,"title":["Models of arithmetic and upper bounds for arithmetic sets"],"prefix":"10.1017","volume":"59","author":[{"given":"Alistair H.","family":"Lachlan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert I.","family":"Soare","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200019642_ref008","unstructured":"Solovay R. M. , Degrees of models of true arithmetic, preliminary version, unpublished manuscript (1983)."},{"key":"S0022481200019642_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1984-0732105-5"},{"key":"S0022481200019642_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(85)90001-6"},{"key":"S0022481200019642_ref001","first-page":"182\u2013191","volume-title":"Proceedings of the U.S.-Israel Workshop on Model Theory in Mathematical Logic: Classification Theory, Chicago, December 15\u201319, 1985 (John Baldwin, editor)","volume":"1292","author":"Knight","year":"1987"},{"key":"S0022481200019642_ref006","first-page":"233\u2013242","volume-title":"Proceedings of the Herbrand Symposium: Logic Colloquium, 1981 (J. Stern, editor)","author":"Marker","year":"1982"},{"key":"S0022481200019642_ref002","first-page":"787\u2013804","volume":"55","author":"Knight","year":"1990","journal-title":"A metatheorem for constructions by finitely many workers"},{"key":"S0022481200019642_ref003","first-page":"425\u2013436","volume":"49","author":"Knight","year":"1984","journal-title":"Two Theorems On Degrees Of Models Of Arithmetic"},{"key":"S0022481200019642_ref007","first-page":"117\u2013121","volume-title":"Recursive Function Theory","volume":"5","author":"Scott","year":"1961"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200019642","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T03:16:48Z","timestamp":1557890208000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200019642\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,9]]},"references-count":8,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1994,9]]}},"alternative-id":["S0022481200019642"],"URL":"https:\/\/doi.org\/10.2307\/2275921","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,9]]}}}