{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T12:07:15Z","timestamp":1759147635402},"reference-count":15,"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":284,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2013,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In reverse mathematics, it is possible to have a curious situation where we know that an implication does not reverse, but appear to have no information on how to weaken the assumption while preserving the conclusion (other than reducing all the way to the tautology of assuming the conclusion). A main cause of this phenomenon is the proof of a<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200000098_inline1\"\/>sentence from the theory<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200000098_inline2\"\/>. Using methods based on the functional interpretation, we introduce a family of weakenings of<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200000098_inline2\"\/>and use them to give new upper bounds for the Nash-Williams Theorem of wqo theory and Menger's Theorem for countable graphs.<\/jats:p>","DOI":"10.2178\/jsl.7802070","type":"journal-article","created":{"date-parts":[[2013,5,15]],"date-time":"2013-05-15T14:11:08Z","timestamp":1368627068000},"page":"459-488","source":"Crossref","is-referenced-by-count":5,"title":["Partial impredicativity in reverse mathematics"],"prefix":"10.1017","volume":"78","author":[{"given":"Henry","family":"Towsner","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200000098_ref005","first-page":"376","volume":"49","author":"Clote","year":"1984","journal-title":"A recursion theoretic analysis of the clopen Ramsey theory"},{"key":"S0022481200000098_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/BF02007558"},{"key":"S0022481200000098_ref011","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)90192-G"},{"key":"S0022481200000098_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71365-X"},{"key":"S0022481200000098_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(98)80020-7"},{"key":"S0022481200000098_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/s001530050095"},{"key":"S0022481200000098_ref003","first-page":"1100","volume":"74","author":"Avigad","year":"2009","journal-title":"Functional interpretation and inductive definitions"},{"key":"S0022481200000098_ref004","first-page":"1","volume":"66","author":"Cholak","year":"2001","journal-title":"On the strength of Ramsey's theorem for pairs"},{"key":"S0022481200000098_ref007","volume-title":"Applied proof theory","author":"Kohlenbach","year":"2008"},{"key":"S0022481200000098_ref008","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1093\/oso\/9780198538622.003.0014","volume-title":"Logic: from foundations to applications","author":"Marcone","year":"1996"},{"key":"S0022481200000098_ref009","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100003844"},{"key":"S0022481200000098_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-012-0269-8"},{"key":"S0022481200000098_ref014","first-page":"961","volume":"53","author":"Simpson","year":"1988","journal-title":"Ordinal numbers and the Hilbert basis theorem"},{"key":"S0022481200000098_ref015","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511581007"},{"key":"S0022481200000098_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(98)80019-0"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200000098","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,10]],"date-time":"2024-05-10T19:09:47Z","timestamp":1715368187000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200000098\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,6]]}},"alternative-id":["S0022481200000098"],"URL":"https:\/\/doi.org\/10.2178\/jsl.7802070","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,6]]}}}