{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T02:36:35Z","timestamp":1774924595962,"version":"3.50.1"},"reference-count":17,"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":6310,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1996,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Models of normal open induction are those normal discretely ordered rings whose nonnegative part satisfy Peano's axioms for open formulas in the language of ordered semirings. (Where normal means integrally closed in its fraction field.)<\/jats:p><jats:p>In 1964 Shepherdson gave a recursive nonstandard model of open induction. His model is not normal and does not have any infinite prime elements.<\/jats:p><jats:p>In this paper we present a recursive nonstandard model of normal open induction with an unbounded set of infinite prime elements.<\/jats:p>","DOI":"10.2307\/2275813","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:59:54Z","timestamp":1146941994000},"page":"1228-1241","source":"Crossref","is-referenced-by-count":13,"title":["A recursive nonstandard model of normal open induction"],"prefix":"10.1017","volume":"61","author":[{"given":"Alessandro","family":"Berarducci","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Margarita","family":"Otero","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200016868_ref015","volume-title":"Algebraic curves","author":"Walker","year":"1950"},{"key":"S0022481200016868_ref017","first-page":"72","volume":"50","author":"Wilmers","year":"1985","journal-title":"Bounded existential induction"},{"key":"S0022481200016868_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0090173"},{"key":"S0022481200016868_ref008","first-page":"779","volume":"55","author":"Otero","year":"1990","journal-title":"On diophantine equations solvable in models of open induction"},{"key":"S0022481200016868_ref010","first-page":"79","article-title":"A nonstandard model for a free variable fragment of number theory","volume":"12","author":"Shepherdson","year":"1964","journal-title":"Bulletin of the Polish Academy of Sciences"},{"key":"S0022481200016868_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(89)90025-0"},{"key":"S0022481200016868_ref001","first-page":"297","article-title":"L'induction pour les formules ouverts n'est pas finiment axiomatisable","volume":"I","author":"Boughattas","year":"1989","journal-title":"Comptes Rendus de l'Acad\u00e9mie des Sciences, Paris"},{"key":"S0022481200016868_ref002","volume-title":"Commutative algebra","author":"Bourbaki","year":"1969"},{"key":"S0022481200016868_ref003","volume-title":"Galois theory","author":"Edwards","year":"1984"},{"key":"S0022481200016868_ref006","unstructured":"Moniri M. , Recursive models of open induction of prescribed finite transcendence degree > 1 with cofinal twin primes, to appear."},{"key":"S0022481200016868_ref007","first-page":"93","article-title":"Tout corp reel clos possede une partie entiere","volume":"I","author":"Mourgues","year":"1992","journal-title":"Comptes Rendus de l'Acad\u00e9mie des Sciences, Paris"},{"key":"S0022481200016868_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)90079-S"},{"key":"S0022481200016868_ref011","first-page":"270","volume-title":"Notices of the American Mathematical Society","author":"Tennenbaum","year":"1959"},{"key":"S0022481200016868_ref013","first-page":"33","article-title":"Which curves over \u2124 have points with coordinates in a discretely ordered ring?","volume":"264","author":"Dries","year":"1980","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200016868_ref014","volume-title":"Modern algebra II","author":"Waerden","year":"1950"},{"key":"S0022481200016868_ref016","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)72011-1"},{"key":"S0022481200016868_ref005","first-page":"403","volume":"47","author":"McAloon","year":"1982","journal-title":"On the complexity of models of arithmetic"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200016868","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T15:59:28Z","timestamp":1557676768000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200016868\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,12]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1996,12]]}},"alternative-id":["S0022481200016868"],"URL":"https:\/\/doi.org\/10.2307\/2275813","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,12]]}}}