{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T15:35:12Z","timestamp":1747150512628,"version":"3.40.5"},"reference-count":17,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T00:00:00Z","timestamp":1648598400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2022,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Given sets  and a regular cardinal \u03bc, let  be the statement that for any function , there are functions  and  such that for all , . In , the statement  is false. However, we show the theory  (which is implied by + \u201c\u201d + \u201c\u03c9<jats:sub>1<\/jats:sub> is measurable\u201d) implies that for every  there is a  such that in some inner model, \u03ba is measurable with Mitchell order .<\/jats:p>","DOI":"10.1002\/malq.202000008","type":"journal-article","created":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T12:47:19Z","timestamp":1648644439000},"page":"202-212","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Bounding 2d functions by products of 1d functions"],"prefix":"10.1002","volume":"68","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3573-4314","authenticated-orcid":false,"given":"Fran\u00e7ois","family":"Dorais","sequence":"first","affiliation":[{"name":"University of Vermont 82 University Place Burlington VT 05405 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6465-0027","authenticated-orcid":false,"given":"Dan","family":"Hathaway","sequence":"additional","affiliation":[{"name":"University of Vermont 82 University Place Burlington VT 05405 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2022,3,30]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5764-9_7"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2009.06.001"},{"key":"e_1_2_8_4_1","unstructured":"C.Dance Contributions to Descriptive Set Theory PhD thesis(University of North Texas 2016)."},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.2307\/1970935"},{"key":"e_1_2_8_6_1","first-page":"195","volume-title":"Lecture Notes in Mathematics","author":"Henle J.","year":"1985"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02771215"},{"volume-title":"Set Theory","year":"2006","author":"Jech T.","key":"e_1_2_8_8_1"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.2178\/jsl.7803020"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0069385"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(77)90006-7"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1987-0869398-2"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5764-9_19"},{"key":"e_1_2_8_14_1","first-page":"209","volume-title":"Studies in Logic and the Foundations of Mathematics Vol. 108","author":"Mitchell W.","year":"1982"},{"key":"e_1_2_8_15_1","unstructured":"W.Mitchell One repeat point gives a closed unbounded ultrafilter on \u03c91 https:\/\/arxiv.org\/abs\/1403.4690(2014)."},{"key":"e_1_2_8_16_1","unstructured":"W.MitchellandE.Schimmerling Covering at limit cardinals of K Preprint (2019)."},{"volume-title":"Lecture Notes in Mathematics Vol. 689","year":"1978","author":"Solovay R.","key":"e_1_2_8_17_1"},{"key":"e_1_2_8_18_1","doi-asserted-by":"publisher","DOI":"10.2307\/2275715"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.202000008","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/malq.202000008","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.202000008","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,25]],"date-time":"2023-08-25T21:46:35Z","timestamp":1692999995000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.202000008"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,30]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,5]]}},"alternative-id":["10.1002\/malq.202000008"],"URL":"https:\/\/doi.org\/10.1002\/malq.202000008","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"type":"print","value":"0942-5616"},{"type":"electronic","value":"1521-3870"}],"subject":[],"published":{"date-parts":[[2022,3,30]]},"assertion":[{"value":"2017-10-14","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-03-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-03-30","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}