{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T12:05:06Z","timestamp":1759147506565},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":6401,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1996,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that the theory <jats:italic>ATR<\/jats:italic><jats:sub>0<\/jats:sub> is equivalent to a second-order generalization of the theory <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200017102_inline1\" \/>. As a result, <jats:italic>ATR<\/jats:italic><jats:sub>0<\/jats:sub> is conservative over <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200017102_inline1\" \/> for arithmetic sentences, though proofs in <jats:italic>ATR<\/jats:italic><jats:sub>0<\/jats:sub> can be much shorter than their <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200017102_inline1\" \/> counterparts.<\/jats:p>","DOI":"10.2307\/2275783","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:59:03Z","timestamp":1146956343000},"page":"768-779","source":"Crossref","is-referenced-by-count":25,"title":["On the relationship between <i>ATR<\/i><sub>0<\/sub> and"],"prefix":"10.1017","volume":"61","author":[{"given":"Jeremy","family":"Avigad","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200017102_ref009","volume-title":"Lecture notes in mathematics 1407","author":"Pohlers","year":"1989"},{"key":"S0022481200017102_ref017","volume-title":"Proof Theory","author":"Simpson","year":"1987"},{"key":"S0022481200017102_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/BF01621477"},{"key":"S0022481200017102_ref013","volume-title":"The handbook of mathematical logic","author":"Schwichtenbero","year":"1991"},{"key":"S0022481200017102_ref007","volume-title":"Set theory","author":"Jech","year":"1978"},{"key":"S0022481200017102_ref006","volume-title":"Theories for admissible sets: A unifying approach to proof theory","author":"J\u00e4ger","year":"1986"},{"key":"S0022481200017102_ref008","volume-title":"The handbook of mathematical logic","author":"Martin","year":"1991"},{"key":"S0022481200017102_ref003","volume-title":"Patras logic symposium","author":"Friedman","year":"1982"},{"key":"S0022481200017102_ref002","volume-title":"Patras logic symposium","author":"Feferman","year":"1982"},{"key":"S0022481200017102_ref010","first-page":"423","volume":"50","author":"Pudl\u00e1k","year":"1985","journal-title":"Cuts, consistency statements, and interpretations"},{"key":"S0022481200017102_ref018","first-page":"113","volume":"59","author":"Simpson","year":"1994","journal-title":"On the strength of K\u00f6nig's duality theorem of countable bipartite graphs"},{"key":"S0022481200017102_ref011","volume-title":"Logic Colloqium '84","author":"Pudl\u00e1k","year":"1986"},{"key":"S0022481200017102_ref015","unstructured":"Simpson Stephen G. , Subsystems of second order arithmetic, preprint."},{"key":"S0022481200017102_ref004","volume-title":"Metamathematics of first-order arithmetic","author":"H\u00e1jek","year":"1991"},{"key":"S0022481200017102_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-66473-1"},{"key":"S0022481200017102_ref001","unstructured":"Avigad Jeremy , Proof-theoretic investigations of subsystems of second-order arithmetic, Ph.d. dissertation , U. C. Berkeley, 1995."},{"key":"S0022481200017102_ref005","unstructured":"Ignjatovic Aleksandar , Fragments of first and second order arithmetic and length of proofs, Ph.d. dissertation , U. C. Berkeley, 1990."},{"key":"S0022481200017102_ref016","volume-title":"Logic Colloqium","volume":"80","author":"Simpson","year":"1982"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200017102","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T20:33:18Z","timestamp":1557693198000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200017102\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,9]]},"references-count":18,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1996,9]]}},"alternative-id":["S0022481200017102"],"URL":"https:\/\/doi.org\/10.2307\/2275783","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,9]]}}}