{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T05:40:39Z","timestamp":1698298839424},"reference-count":2,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":4334,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1995,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove the following theorem: Let \u03c6(<jats:italic>x<\/jats:italic>) be a formula in the language of the theory PA<jats:sup>\u2212<\/jats:sup> of discretely ordered commutative rings with unit of the form \u2203y\u03c6\u2032(<jats:italic>x,y<\/jats:italic>) with \u03c6\u2032 and let \u2208 \u0394<jats:sub>0<\/jats:sub> and let <jats:italic>f<\/jats:italic>\u03c6: \u2115 \u2192 \u2115 such that <jats:italic>f<\/jats:italic><jats:sub>\u03c6<\/jats:sub>(<jats:italic>x<\/jats:italic>) = <jats:italic>y<\/jats:italic> iff \u03c6\u2032(<jats:italic>x,y<\/jats:italic>) &amp; (\u2200<jats:italic>z<\/jats:italic> &lt; <jats:italic>y<\/jats:italic>) \u03c6\u2032(<jats:italic>x,z<\/jats:italic>). If I \u220f<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-stack-2.gif\" xlink:title=\"urn:x-wiley:09425616:media:MALQ19950410111:tex2gif-stack-2\" \/> \u2208(\u2200<jats:italic>x<\/jats:italic> \u2265 0), \u03c6 then there exists a natural number <jats:italic>K<\/jats:italic> such that I \u220f<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-stack-3.gif\" xlink:title=\"urn:x-wiley:09425616:media:MALQ19950410111:tex2gif-stack-3\" \/> \u22a2 \u2203y\u2200x(<jats:italic>x<\/jats:italic> &gt; <jats:italic>y<\/jats:italic> \u27f9 \u0192\u03c6(<jats:italic>x<\/jats:italic>) &lt; <jats:italic>x<\/jats:italic><jats:sup><jats:italic>K<\/jats:italic><\/jats:sup>). Here I \u220f<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-stack-4.gif\" xlink:title=\"urn:x-wiley:09425616:media:MALQ19950410111:tex2gif-stack-4\" \/><jats:sub>1<\/jats:sub><jats:sup>\u2212<\/jats:sup> denotes the theory PA<jats:sup>\u2212<\/jats:sup> plus the scheme of induction for formulas \u03c6(<jats:italic>x<\/jats:italic>) of the form \u2200<jats:italic>y<\/jats:italic>\u03c6\u2032(<jats:italic>x<\/jats:italic>,<jats:italic>y<\/jats:italic>) (with \u03c6\u2032) with \u03c6\u2032 \u2208 \u0394<jats:sub>0<\/jats:sub>.<\/jats:p>","DOI":"10.1002\/malq.19950410111","type":"journal-article","created":{"date-parts":[[2007,6,3]],"date-time":"2007-06-03T01:58:50Z","timestamp":1180835930000},"page":"135-137","source":"Crossref","is-referenced-by-count":5,"title":["On \u03a3<sub>1<\/sub>\u2010definable Functions Provably Total in I \u220f"],"prefix":"10.1002","volume":"41","author":[{"given":"Teresa","family":"Bigorajska","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","first-page":"189","DOI":"10.4064\/fm-132-3-189-194","article-title":"Functions provably total in I\u03a31.","volume":"132","author":"Adamowicz Z.","year":"1989","journal-title":"Fund. Math."},{"key":"e_1_2_1_3_2","unstructured":"Kaye R. Diophantine and parameter\u2010free induction. Doctoral Thesis University of Manchester 1987."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19950410111","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19950410111","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T17:57:57Z","timestamp":1698256677000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19950410111"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,1]]},"references-count":2,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1995,1]]}},"alternative-id":["10.1002\/malq.19950410111"],"URL":"https:\/\/doi.org\/10.1002\/malq.19950410111","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,1]]}}}