{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T18:09:37Z","timestamp":1726250977890},"reference-count":28,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4394,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this article we provide wellordering proofs for metapredicative systems of explicit mathematics and admissible set theory featuring suitable axioms about the Mahloness of the underlying universe of discourse. In particular, it is shown that in the corresponding theories EMA of explicit mathematics and KPm<jats:sup>0<\/jats:sup> of admissible set theory, transfinite induction along initial segments of the ordinal <jats:italic>\u03c6\u03c9<\/jats:italic>00, for <jats:italic>\u03c6<\/jats:italic> being a ternary Veblen function, is derivable. This reveals that the upper bounds given for these two systems in the paper J\u00e4ger and Strahm [11] are indeed sharp.<\/jats:p>","DOI":"10.2178\/jsl\/1190150043","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T19:12:10Z","timestamp":1197573130000},"page":"260-278","source":"Crossref","is-referenced-by-count":9,"title":["Wellordering proofs for metapredicative Mahlo"],"prefix":"10.1017","volume":"67","author":[{"given":"Thomas","family":"Strahm","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009981_ref023","unstructured":"R\u00fcede C. , Metapredicative subsystems of analysis, Ph.D. thesis , Institut f\u00fcr Informatik und angewandte Mathematik, Univerist\u00e4t Bern, 2000."},{"key":"S0022481200009981_ref028","volume-title":"Constructivism in Mathematics","volume":"I","author":"Troelstra","year":"1988"},{"key":"S0022481200009981_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(95)00028-3"},{"key":"S0022481200009981_ref007","first-page":"867","volume":"49","author":"J\u00e4ger","year":"1984","journal-title":"The strength of admissibility without foundation"},{"key":"S0022481200009981_ref017","doi-asserted-by":"publisher","DOI":"10.1007\/BF01275469"},{"key":"S0022481200009981_ref016","doi-asserted-by":"publisher","DOI":"10.1007\/BF01621475"},{"key":"S0022481200009981_ref019","doi-asserted-by":"publisher","DOI":"10.1007\/s001530000051"},{"key":"S0022481200009981_ref021","unstructured":"R\u00fcede C. , The proof-theoretic analysis of \u03a31 1 transfinite dependent choice, Submitted for publication."},{"key":"S0022481200009981_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0062852"},{"key":"S0022481200009981_ref008","first-page":"53","volume":"64","author":"J\u00e4ger","year":"1999","journal-title":"The proof-theoretic analysis of transfinitely iterated fixed point theories"},{"key":"S0022481200009981_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71364-8"},{"key":"S0022481200009981_ref025","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-66473-1"},{"key":"S0022481200009981_ref012","volume-title":"Annals of Pure and Applied Logic","author":"J\u00e4ger"},{"key":"S0022481200009981_ref010","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1007\/s001530050161","article-title":"Fixed point theories and dependent choice","volume":"39","author":"J\u00e4ger","year":"2000","journal-title":"Archive for Mathematical Logic"},{"key":"S0022481200009981_ref018","doi-asserted-by":"publisher","DOI":"10.1007\/s001530050001"},{"key":"S0022481200009981_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-46825-7"},{"key":"S0022481200009981_ref005","first-page":"1","volume":"56","author":"Feferman","year":"1991","journal-title":"Reflecting on incompleteness"},{"key":"S0022481200009981_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(00)00057-9"},{"key":"S0022481200009981_ref011","first-page":"935","volume":"66","author":"J\u00e4ger","year":"2001","journal-title":"Upper bounds for metapredicative Mahlo in explicit mathematics and admissible set theory"},{"key":"S0022481200009981_ref014","unstructured":"Marzetta M. , Predicative theories of types and names, Ph.D. thesis , Institut f\u00fcr Informatik und angewandte Mathematik, Universit\u00e4t Bern, 1993."},{"key":"S0022481200009981_ref020","unstructured":"R\u00fcede C. , Metapredicative subsystems of analysis, Submitted for publication."},{"key":"S0022481200009981_ref022","unstructured":"R\u00fcede C. , Universes in metapredicative analysis. Submitted for publication."},{"key":"S0022481200009981_ref024","doi-asserted-by":"publisher","DOI":"10.1007\/BF01361109"},{"key":"S0022481200009981_ref026","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107325944.016"},{"key":"S0022481200009981_ref027","first-page":"449","volume-title":"Logic Colloquium '98","volume":"13","author":"Strahm","year":"2000"},{"key":"S0022481200009981_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-68952-9"},{"key":"S0022481200009981_ref003","first-page":"159","volume-title":"Logic Colloquium '78","author":"Feferman","year":"1979"},{"key":"S0022481200009981_ref013","unstructured":"Kahle R. , Applikative theorien und frege-strukturen, Ph.D. thesis , Institut f\u00fcr Informatik und angewandte Mathematik, Universit\u00e4t Bern, 1997."}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009981","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T01:34:51Z","timestamp":1557192891000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009981\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,3]]},"references-count":28,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2002,3]]}},"alternative-id":["S0022481200009981"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150043","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,3]]}}}