{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T02:36:40Z","timestamp":1774924600261,"version":"3.50.1"},"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":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>We consider IOpen, the subsystem of PA (Peano Arithmetic) with the induction scheme restricted to quantifier-free formulas.<\/jats:p><jats:p>We prove that each model of IOpen can be embedded in a model where the equation <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200026141_inline1\"\/> has a solution. The main lemma states that there is <jats:italic>no<\/jats:italic> polynomial <jats:italic>f{x,y)<\/jats:italic> with coefficients in a (nonstandard) DOR <jats:italic>M<\/jats:italic> such that \u2223<jats:italic>f(x,y)<\/jats:italic> \u2223 &lt; 1 for every <jats:italic>(x,y)<\/jats:italic> \u0404 <jats:italic>C<\/jats:italic>, where <jats:italic>C<\/jats:italic> is the curve defined on the real closure of <jats:italic>M<\/jats:italic> by <jats:italic>C<\/jats:italic>: <jats:italic>x<\/jats:italic><jats:sup>2<\/jats:sup> + <jats:italic>y<\/jats:italic><jats:sup>2<\/jats:sup> = <jats:italic>a<\/jats:italic> and <jats:italic>a<\/jats:italic> &gt; 0 is a nonstandard element of <jats:italic>M<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2274664","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:35:29Z","timestamp":1146954929000},"page":"779-786","source":"Crossref","is-referenced-by-count":6,"title":["On Diophantine equations solvable in models of open induction"],"prefix":"10.1017","volume":"55","author":[{"given":"Margarita","family":"Otero","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200026141_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)72011-1"},{"key":"S0022481200026141_ref004","first-page":"79","article-title":"A non-standard model for a free variable fragment of number theory","volume":"12","author":"Shepherdson","year":"1964","journal-title":"Bulletin de l'Acad\u00e9mie Polonaise des Sciences, S\u00e9rie des Sciences Math\u00e9matiques, Astronomiques et Physiques"},{"key":"S0022481200026141_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0090173"},{"key":"S0022481200026141_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(89)90025-0"},{"key":"S0022481200026141_ref001","volume-title":"Number theory","author":"Borevich","year":"1968"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200026141","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T21:13:48Z","timestamp":1558214028000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200026141\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,6]]},"references-count":5,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1990,6]]}},"alternative-id":["S0022481200026141"],"URL":"https:\/\/doi.org\/10.2307\/2274664","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,6]]}}}