{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T00:12:53Z","timestamp":1782259973131,"version":"3.54.5"},"reference-count":0,"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":14894,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1973,6]]},"abstract":"<jats:p>Combinations of capital letters (e.g., <jats:italic>G, EVEN<\/jats:italic>) will be used as names of formulas of Peano arithmetic, <jats:italic>x, y, z<\/jats:italic> will be variables. Let <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200077872_inline1\"\/> be a model for Peano arithmetic. The names of formulas with a bar (e.g., <jats:italic>G<jats:sup>\u2212<\/jats:sup>, EVEN<jats:sup>\u2212<\/jats:sup>(x)<\/jats:italic>) will denote the relations defined by the formulas in <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200077872_inline1\"\/>. The elements of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200077872_inline1\"\/> are called numbers.<\/jats:p><jats:p>By a finite sequence of numbers \u3008<jats:italic>a<\/jats:italic><jats:sub>0<\/jats:sub>, \u2026, <jats:italic>a<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>\u3009 we mean a number <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200077872_inline2\"\/><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200077872_inline3\"\/>. Note that <jats:italic>n P<jats:sub>i<\/jats:sub><\/jats:italic>'s and <jats:italic>a<jats:sub>i<\/jats:sub><\/jats:italic>'s can be nonstandard elements and therefore \u201cfinite,\u201d and all concepts which will use it are not absolute but relative to <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200077872_inline1\"\/>.<\/jats:p>","DOI":"10.2307\/2272063","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:22:43Z","timestamp":1146950563000},"page":"291-292","source":"Crossref","is-referenced-by-count":13,"title":["Discernible elements in models for Peano arithmetic"],"prefix":"10.1017","volume":"38","author":[{"given":"Andrzej","family":"Ehrenfeucht","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200077872","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T19:54:38Z","timestamp":1559246078000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200077872\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1973,6]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1973,6]]}},"alternative-id":["S0022481200077872"],"URL":"https:\/\/doi.org\/10.2307\/2272063","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1973,6]]}}}