{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T04:46:48Z","timestamp":1776919608682,"version":"3.51.2"},"reference-count":10,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2018,7,18]],"date-time":"2018-07-18T00:00:00Z","timestamp":1531872000000},"content-version":"vor","delay-in-days":17,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["LU2020\/1\u20101"],"award-info":[{"award-number":["LU2020\/1\u20101"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2018,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study the influence of the existence of large cardinals on the existence of wellorderings of power sets of infinite cardinals \u03ba with the property that the collection of all initial segments of the wellordering is definable by a \u03a3<jats:sub>1<\/jats:sub>\u2010formula with parameter \u03ba. A short argument shows that the existence of a measurable cardinal \u03b4 implies that such wellorderings do not exist at \u03b4\u2010inaccessible cardinals of cofinality not equal to \u03b4 and their successors. In contrast, our main result shows that these wellorderings exist at all other uncountable cardinals in the minimal model containing a measurable cardinal. In addition, we show that measurability is the smallest large cardinal property that imposes restrictions on the existence of such wellorderings at uncountable cardinals. Finally, we generalise the above result to the minimal model containing two measurable cardinals.<\/jats:p>","DOI":"10.1002\/malq.201700018","type":"journal-article","created":{"date-parts":[[2018,7,18]],"date-time":"2018-07-18T22:54:31Z","timestamp":1531954471000},"page":"207-217","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Measurable cardinals and good \u2010wellorderings"],"prefix":"10.1002","volume":"64","author":[{"given":"Philipp","family":"L\u00fccke","sequence":"first","affiliation":[{"name":"Mathematisches Institut Universit\u00e4t Bonn Endenicher Allee 60 53115 Bonn Germany"}]},{"given":"Philipp","family":"Schlicht","sequence":"additional","affiliation":[{"name":"Mathematisches Institut Universit\u00e4t Bonn Endenicher Allee 60 53115 Bonn Germany"}]}],"member":"311","published-online":{"date-parts":[[2018,7,18]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(81)90011-5"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(83)90020-9"},{"key":"e_1_2_7_4_1","volume-title":"Set Theory, The Third Millenium Edition","author":"Jech T.","year":"2003"},{"key":"e_1_2_7_5_1","volume-title":"The Higher Infinite","author":"Kanamori A.","year":"2003"},{"key":"e_1_2_7_6_1","unstructured":"P.Koepke A theory of short core models and some applications PhD thesis (Albert\u2010Ludwigs\u2010Universit\u00e4t Freiburg 1984)."},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(88)90026-7"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(70)90013-6"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2017.36"},{"key":"e_1_2_7_10_1","doi-asserted-by":"publisher","DOI":"10.2307\/2272343"},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/013.1\/0278937"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201700018","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201700018","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,17]],"date-time":"2023-09-17T19:25:19Z","timestamp":1694978719000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201700018"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7]]},"references-count":10,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,7]]}},"alternative-id":["10.1002\/malq.201700018"],"URL":"https:\/\/doi.org\/10.1002\/malq.201700018","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,7]]},"assertion":[{"value":"2017-04-03","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-12-10","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-07-18","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}