{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T12:58:50Z","timestamp":1773147530227,"version":"3.50.1"},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":466,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2012,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Assuming 2<jats:sup>\u2135<jats:sub>0<\/jats:sub><\/jats:sup> = \u2135<jats:sub>1<\/jats:sub> and 2<jats:sup>\u2135<jats:sub>1<\/jats:sub><\/jats:sup> = \u2135<jats:sub>2<\/jats:sub>, we build a partial order that forces the existence of a well-order of <jats:italic>H<\/jats:italic>(<jats:italic>\u03c9<\/jats:italic><jats:sub>2<\/jats:sub>) lightface definable over \u27e8<jats:italic>H<\/jats:italic>(<jats:italic>\u03c9<\/jats:italic><jats:sub>1<\/jats:sub>), \u2208\u27e9 and that preserves cardinal exponentiation and cofinalities.<\/jats:p>","DOI":"10.2178\/jsl.7704030","type":"journal-article","created":{"date-parts":[[2012,11,2]],"date-time":"2012-11-02T19:23:52Z","timestamp":1351884232000},"page":"1101-1121","source":"Crossref","is-referenced-by-count":4,"title":["Definable well-orders of <i>H<\/i>(<i>\u03c9<\/i><sub>2<\/sub>) and GCH"],"prefix":"10.1017","volume":"77","author":[{"given":"David","family":"Asper\u00f3","sequence":"first","affiliation":[]},{"given":"Sy-David","family":"Friedman","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200001134_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2005.11.006"},{"key":"S0022481200001134_ref008","doi-asserted-by":"publisher","DOI":"10.4064\/fm215-2-3"},{"key":"S0022481200001134_ref009","unstructured":"[J] Jech Thomas , Set theory, Springer, 2002."},{"key":"S0022481200001134_ref006","first-page":"641","volume":"74","author":"Brooke-Taylor","year":"2009","journal-title":"Large cardinals and definable well-orderings of the universe"},{"key":"S0022481200001134_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2008.07.006"},{"key":"S0022481200001134_ref001","first-page":"579","volume":"67","author":"Abraham","year":"2002","journal-title":"Coding with ladders a well ordering of the reals"},{"key":"S0022481200001134_ref004","volume-title":"Computational prospects of infinity, Part II: Presented talks","volume":"15","author":"Asper\u00f3","year":"2008"},{"key":"S0022481200001134_ref003","unstructured":"[As2] Asper\u00f3 David , Coding into H(\u03ba+) without parameters, unpublished note, 2006."},{"key":"S0022481200001134_ref007","unstructured":"[F] Friedman Sy-David , Forcing condensation, notes, 2008."},{"key":"S0022481200001134_ref010","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061305000407"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200001134","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,24]],"date-time":"2019-04-24T21:27:37Z","timestamp":1556141257000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200001134\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,12]]}},"alternative-id":["S0022481200001134"],"URL":"https:\/\/doi.org\/10.2178\/jsl.7704030","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12]]}}}