{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T15:35:06Z","timestamp":1747150506507,"version":"3.40.5"},"reference-count":6,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2019,12,12]],"date-time":"2019-12-12T00:00:00Z","timestamp":1576108800000},"content-version":"vor","delay-in-days":11,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"name":"CUNY Research Foundation","award":["PSC-CUNY grant 69573-00 47"],"award-info":[{"award-number":["PSC-CUNY grant 69573-00 47"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2019,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The assertion that every definable set has a definable element is equivalent over  to the principle , and indeed, we prove, so is the assertion merely that every \u03a0<jats:sub>2<\/jats:sub>\u2010definable set has an ordinal\u2010definable element. Meanwhile, every model of  has a forcing extension satisfying  in which every \u03a3<jats:sub>2<\/jats:sub>\u2010definable set has an ordinal\u2010definable element. Similar results hold for  and  and other natural instances of .<\/jats:p>","DOI":"10.1002\/malq.201700035","type":"journal-article","created":{"date-parts":[[2019,12,12]],"date-time":"2019-12-12T11:05:42Z","timestamp":1576148742000},"page":"407-411","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["When does every definable nonempty set have a definable element?"],"prefix":"10.1002","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3573-4314","authenticated-orcid":false,"given":"Fran\u00e7ois G.","family":"Dorais","sequence":"first","affiliation":[{"name":"Department of Mathematics University of Vermont Burlington VT 05405 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joel David","family":"Hamkins","sequence":"additional","affiliation":[{"name":"University College Oxford University High Street Oxford OX1 4BH England"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2019,12,12]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1052669062"},{"key":"e_1_2_6_3_1","unstructured":"J. D.Hamkins Answer to question \u201cDefinable collections without definable members (inZF)\u201d 2 January 2010 MathOverflow Question 10415 (2010)."},{"key":"e_1_2_6_4_1","unstructured":"J. D.Hamkins Local properties in set theory blog posting on the author's webpage 24 June 2014."},{"key":"e_1_2_6_5_1","unstructured":"J. D.Hamkins Answer to question \u201cIs it consistent withZFC(orZF) that every definable family of sets has at least one definable member?\u201d 12 September 2014 MathOverflow Question 180734 (2014)."},{"key":"e_1_2_6_6_1","unstructured":"J. D.Hamkins Answer to question \u201cCanV\u2260HOD if every \u03a32\u2010definable set has an ordinal\u2010definable element?\u201d 14 September 2014 MathOverflow Question 180850 (2014)."},{"key":"e_1_2_6_7_1","doi-asserted-by":"publisher","DOI":"10.2178\/jsl.7801090"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201700035","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201700035","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/malq.201700035","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201700035","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,7]],"date-time":"2023-09-07T22:12:13Z","timestamp":1694124733000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201700035"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12]]},"references-count":6,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["10.1002\/malq.201700035"],"URL":"https:\/\/doi.org\/10.1002\/malq.201700035","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"type":"print","value":"0942-5616"},{"type":"electronic","value":"1521-3870"}],"subject":[],"published":{"date-parts":[[2019,12]]},"assertion":[{"value":"2017-06-21","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-03-18","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-12-12","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}