{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T10:09:34Z","timestamp":1775470174873,"version":"3.50.1"},"reference-count":25,"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":11607,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1982,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>P<\/jats:italic><jats:sub>0<\/jats:sub> be the subsystem of Peano arithmetic obtained by restricting induction to bounded quantifier formulas. Let <jats:italic>M<\/jats:italic> be a countable, nonstandard model of <jats:italic>P<\/jats:italic><jats:sub>0<\/jats:sub> whose domain we suppose to be the standard integers. Let <jats:italic>T<\/jats:italic> be a recursively enumerable extension of Peano arithmetic all of whose existential consequences are satisfied in the standard model. Then there is an initial segment <jats:italic>M<\/jats:italic>\u2032 of <jats:italic>M<\/jats:italic> which is a model of <jats:italic>T<\/jats:italic> such that the complete diagram of <jats:italic>M<\/jats:italic>\u2032 is Turing reducible to the atomic diagram of <jats:italic>M<\/jats:italic>. Moreover, neither the addition nor the multiplication of <jats:italic>M<\/jats:italic> is recursive.<\/jats:p>","DOI":"10.2307\/2273150","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:59:42Z","timestamp":1146952782000},"page":"403-415","source":"Crossref","is-referenced-by-count":20,"title":["On the complexity of models of arithmetic"],"prefix":"10.1017","volume":"47","author":[{"given":"Kenneth","family":"McAloon","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200044327_ref023","volume-title":"A handbook of mathematical logic","author":"Paris","year":"1978"},{"key":"S0022481200044327_ref017","volume-title":"Mod\u00e8les de l'arithm\u00e9tique","author":"McAloon","year":"1980"},{"key":"S0022481200044327_ref014","unstructured":"Lessan H. , Models of arithmetic, Thesis, Manchester, 1978."},{"key":"S0022481200044327_ref011","volume-title":"Fundamenta Mathematicae","author":"Kirby"},{"key":"S0022481200044327_ref010","volume-title":"Mod\u00e8les de l'arithm\u00e9tique","author":"Kirby","year":"1980"},{"key":"S0022481200044327_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BF00262039"},{"key":"S0022481200044327_ref008","volume-title":"Lecture Notes in Mathematics","volume":"454","author":"Hirschfeld","year":"1975"},{"key":"S0022481200044327_ref004","first-page":"107","article-title":"Strong models for arithmetic","volume":"14","author":"Ehrenfeucht","year":"1966","journal-title":"Bulletin de l'Acad\u00e9mie Polonaise des Sciences. S\u00e9rie des Sciences Math\u00e9matiques, Astronomiques et Physiques"},{"key":"S0022481200044327_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0095657"},{"key":"S0022481200044327_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0067653"},{"key":"S0022481200044327_ref007","first-page":"515","volume":"42","author":"Hajek","year":"1977","journal-title":"Experimental logics and \u03a030-theories"},{"key":"S0022481200044327_ref013","volume-title":"Mod\u00e8les de l'arithm\u00e9tique","author":"Lascar","year":"1980"},{"key":"S0022481200044327_ref016","volume-title":"Logic, philosophy and methodology of science, VI","author":"Macintyre"},{"key":"S0022481200044327_ref005","volume-title":"Cambridge Summer School in Mathematical Logic","volume":"337","author":"Friedman","year":"1973"},{"key":"S0022481200044327_ref020","first-page":"725","volume":"43","author":"Paris","year":"1978","journal-title":"Some independence results for Peano arithmetic"},{"key":"S0022481200044327_ref019","volume-title":"Colloque International de Logique","author":"McAloon","year":"1977"},{"key":"S0022481200044327_ref025","first-page":"207","article-title":"Non-archimedean models for arithmetic","volume":"6","author":"Tennenbaum","year":"1959","journal-title":"Notices of the American Mathematical Society"},{"key":"S0022481200044327_ref003","unstructured":"Dimttracopoulos G. , Matijasevic's theorem and fragments of arithmetic, Thesis, Manchester, 1980."},{"key":"S0022481200044327_ref006","volume-title":"Conference in Mathematical Logic-London","volume":"255","author":"Gaifman","year":"1970"},{"key":"S0022481200044327_ref002","volume-title":"Proceedings of Logic Colloquium","author":"Cegielski","year":"1980"},{"key":"S0022481200044327_ref021","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0095667"},{"key":"S0022481200044327_ref024","volume-title":"Handbook of mathematical logic","author":"Simpson","year":"1978"},{"key":"S0022481200044327_ref022","volume-title":"Theory of recursive functions and effective computability","author":"Rogers","year":"1967"},{"key":"S0022481200044327_ref018","volume-title":"S\u00e9minaire Bourbaki 1977-78, Lecture Notes in Mathematics","author":"McAloon"},{"key":"S0022481200044327_ref015","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1978-0491158-5"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200044327","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T21:16:20Z","timestamp":1558732580000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200044327\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,6]]},"references-count":25,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1982,6]]}},"alternative-id":["S0022481200044327"],"URL":"https:\/\/doi.org\/10.2307\/2273150","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,6]]}}}