{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T10:54:37Z","timestamp":1649156077922},"reference-count":5,"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":6493,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1996,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that a necessary and sufficient condition for a countable set <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200017448_inline1\" \/> of sets of integers to be equal to the algebra of all sets of integers definable in a nonstandard elementary extension of <jats:italic>\u03c9<\/jats:italic> by a formula of the <jats:bold>PA<\/jats:bold> language which may include the standardness predicate but does not contain nonstandard parameters, is as follows: <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200017448_inline1\" \/> is closed under arithmetical definability and contains 0<jats:sup>(<jats:italic>\u03c9<\/jats:italic>)<\/jats:sup> the set of all (G\u00f6del numbers of) true arithmetical sentences.<\/jats:p><jats:p>Some results related to definability of sets of integers in elementary extensions of <jats:italic>\u03c9<\/jats:italic> are included.<\/jats:p>","DOI":"10.2307\/2275677","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:58:29Z","timestamp":1146941909000},"page":"586-607","source":"Crossref","is-referenced-by-count":0,"title":["On external Scott algebras in nonstandard models of Peano arithmetic"],"prefix":"10.1017","volume":"61","author":[{"given":"Vladimir","family":"Kanovei","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200017448_ref004","volume-title":"Oxford logic guides","volume":"15","author":"Kaye","year":"1991"},{"key":"S0022481200017448_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/005\/0141595"},{"key":"S0022481200017448_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12898-5"},{"key":"S0022481200017448_ref003","doi-asserted-by":"publisher","DOI":"10.1070\/IM1980v015n03ABEH001258"},{"key":"S0022481200017448_ref001","unstructured":"Harrington L. , The constructible reals can be anything, a preprint dated May 1974 with several addendums dated up to 10 1975."}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200017448","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T17:28:57Z","timestamp":1557682137000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200017448\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,6]]},"references-count":5,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1996,6]]}},"alternative-id":["S0022481200017448"],"URL":"https:\/\/doi.org\/10.2307\/2275677","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,6]]}}}