{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,24]],"date-time":"2023-09-24T04:25:27Z","timestamp":1695529527037},"reference-count":7,"publisher":"Wiley","issue":"1-2","license":[{"start":{"date-parts":[[2018,4,17]],"date-time":"2018-04-17T00:00:00Z","timestamp":1523923200000},"content-version":"vor","delay-in-days":16,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["338821"],"award-info":[{"award-number":["338821"]}],"id":[{"id":"10.13039\/501100000781","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":[[2018,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We construct a model satisfying <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600003-math-0001.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600003:malq201600003-math-0001\" \/> \u201c\u03ba is quasi measurable\u201d. Here, we call \u03ba quasi measurable if there is an \u2135<jats:sub>1<\/jats:sub>\u2010saturated \u03ba\u2010additive ideal <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600003-math-0002.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600003:malq201600003-math-0002\" \/> on \u03ba. We also show that, in this model, forcing with <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600003-math-0003.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600003:malq201600003-math-0003\" \/> adds one but not \u03ba Cohen reals. We introduce a weak club principle and use it to show that, consistently, for some \u2135<jats:sub>1<\/jats:sub>\u2010saturated \u03ba\u2010additive ideal <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600003-math-0004.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600003:malq201600003-math-0004\" \/> on \u03ba, forcing with <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600003-math-0005.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600003:malq201600003-math-0005\" \/> adds one but not \u03ba random reals.<\/jats:p>","DOI":"10.1002\/malq.201600003","type":"journal-article","created":{"date-parts":[[2018,4,17]],"date-time":"2018-04-17T08:30:33Z","timestamp":1523953833000},"page":"44-48","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Clubs on quasi measurable cardinals"],"prefix":"10.1002","volume":"64","author":[{"given":"Ashutosh","family":"Kumar","sequence":"first","affiliation":[{"name":"Einstein Institute of Mathematics The Hebrew University of Jerusalem Edmond J Safra Campus, Givat Ram Jerusalem 91904 Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saharon","family":"Shelah","sequence":"additional","affiliation":[{"name":"Einstein Institute of Mathematics The Hebrew University of Jerusalem Edmond J Safra Campus, Givat Ram Jerusalem 91904 Israel"},{"name":"Department of Mathematics, Rutgers The State University of New Jersey Hill Center\u2010Busch Campus, 110 Frelinghuysen Road Piscataway NJ 08854\u20108019 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,4,17]]},"reference":[{"key":"e_1_2_6_2_1","first-page":"151","volume-title":"Set Theory of the Reals","author":"Fremlin D. H.","year":"1993"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02772658"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02772619"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2014.05.001"},{"key":"e_1_2_6_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2014.06.015"},{"key":"e_1_2_6_7_1","unstructured":"A.Kumar S.Shelah RVM RVC revisited: Clubs and Lusin sets submitted."},{"key":"e_1_2_6_8_1","unstructured":"K.P\u0159\u00edkr\u00fd Changing Measurable into Accessible Cardinals Dissertationes Mathematicae Vol.68(Pa\u0144stwowe Wydawnictwo Naukowe 1970)."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201600003","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201600003","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,23]],"date-time":"2023-09-23T22:18:16Z","timestamp":1695507496000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201600003"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4]]},"references-count":7,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2018,4]]}},"alternative-id":["10.1002\/malq.201600003"],"URL":"https:\/\/doi.org\/10.1002\/malq.201600003","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4]]},"assertion":[{"value":"2016-01-08","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-04-03","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-04-17","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}