{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T00:38:13Z","timestamp":1649032693276},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,1,15]],"date-time":"2014-01-15T00:00:00Z","timestamp":1389744000000},"content-version":"unspecified","delay-in-days":2512,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log."],"published-print":{"date-parts":[[2007,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce a nonstandard arithmetic NQA<jats:sup>\u2212<\/jats:sup> based on the theory developed by R. Chuaqui and P. Suppes in [2] (we will denote it by NQA<jats:sup>+<\/jats:sup>), with a weakened external open minimization schema. A finitary consistency proof for NQA<jats:sup>\u2212<\/jats:sup> formalizable in PRA is presented. We also show interesting facts about the strength of the theories NQA<jats:sup>\u2212<\/jats:sup>and NQA<jats:sup>+<\/jats:sup>; NQA<jats:sup>\u2212<\/jats:sup>is mutually interpretable with I\u0394<jats:sub>0<\/jats:sub> + EXP, and on the other hand, NQA<jats:sup>+<\/jats:sup>interprets the theories I\u03a3<jats:sub>1<\/jats:sub> and WKL<jats:sub>0<\/jats:sub>.<\/jats:p>","DOI":"10.2178\/bsl\/1174668218","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T09:55:07Z","timestamp":1197539707000},"page":"54-70","source":"Crossref","is-referenced-by-count":4,"title":["Fragment of Nonstandard Analysis with a Finitary Consistency Proof"],"prefix":"10.1017","volume":"13","author":[{"given":"Michal","family":"R\u00f6ssler","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Emil","family":"Je\u0159\u00e1bek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S1079898600002353_ref007","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1977-14398-X"},{"key":"S1079898600002353_ref010","volume-title":"Mathematical logic","author":"Shoenfield","year":"1967"},{"key":"S1079898600002353_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22156-3"},{"key":"S1079898600002353_ref003","doi-asserted-by":"crossref","first-page":"35","DOI":"10.4064\/fm-49-1-35-92","article-title":"Arithmetization of metamathematics in a general setting","volume":"49","author":"Feferman","year":"1960","journal-title":"Fundamenta Mathematicae"},{"key":"S1079898600002353_ref015","volume-title":"Mathematics in the Alternative Set Theory","author":"Vop\u011bnka","year":"1979"},{"key":"S1079898600002353_ref013","doi-asserted-by":"publisher","DOI":"10.2307\/2026089"},{"key":"S1079898600002353_ref011","volume-title":"Klasick\u00e1 matematick\u00e1 logika","author":"Sochor","year":"2001"},{"key":"S1079898600002353_ref008","doi-asserted-by":"publisher","DOI":"10.2307\/2274231"},{"key":"S1079898600002353_ref009","volume-title":"Non-standard analysis","author":"Robinson","year":"1966"},{"key":"S1079898600002353_ref016","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026247421383"},{"key":"S1079898600002353_ref014","first-page":"307","volume-title":"Advances in modal logic '96","author":"Visser","year":"1998"},{"key":"S1079898600002353_ref012","first-page":"1","article-title":"A finitarily consistent free-variable positive fragment of infinitesimal analysis","volume":"38","author":"Suppes","year":"1993","journal-title":"Notas de Logica Matematica"},{"key":"S1079898600002353_ref006","doi-asserted-by":"publisher","DOI":"10.2307\/2273942"},{"key":"S1079898600002353_ref001","doi-asserted-by":"publisher","DOI":"10.2307\/2275304"},{"key":"S1079898600002353_ref004","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1190150098"},{"key":"S1079898600002353_ref002","doi-asserted-by":"publisher","DOI":"10.2307\/2275512"}],"container-title":["Bulletin of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1079898600002353","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T20:09:11Z","timestamp":1556741351000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1079898600002353\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,3]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2007,3]]}},"alternative-id":["S1079898600002353"],"URL":"https:\/\/doi.org\/10.2178\/bsl\/1174668218","relation":{},"ISSN":["1079-8986","1943-5894"],"issn-type":[{"value":"1079-8986","type":"print"},{"value":"1943-5894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,3]]}}}