{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T15:33:01Z","timestamp":1747150381379,"version":"3.40.5"},"reference-count":14,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T00:00:00Z","timestamp":1721001600000},"content-version":"vor","delay-in-days":75,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11426188","11601443","11771311"],"award-info":[{"award-number":["11426188","11601443","11771311"]}],"id":[{"id":"10.13039\/501100001809","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":[[2024,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that for every ultrafilter  on  there exists a filter  on  which is \u2010Menger and . We show that in the Cohen model there exists such  which are tall by using a construction of Nyikos's [10]. These answer a question of Das [2, Problem 7]. We prove that there is a Menger filter of character  that is not Hurewicz in the \u2010Cohen model where  is uncountable regular. This shows that the positive answer to a question of Hern\u00e1ndez\u2010Guti\u00e9rrez and Szeptycki [3, Question 2.8] is consistent with . We also study the filter  generated by the set of mutually Cohen reals in the \u2010Cohen model. We prove that  and  and every \u2010dominating family in the ground model is \u2010unbounded in extension. Two questions are\u00a0posed.<\/jats:p>","DOI":"10.1002\/malq.202300008","type":"journal-article","created":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T09:10:32Z","timestamp":1721034632000},"page":"224-232","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Filter\u2010Menger set of reals in Cohen extensions"],"prefix":"10.1002","volume":"70","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1964-8099","authenticated-orcid":false,"given":"Hang","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics Southwest Jiaotong University  Chengdu China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuguo","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mathematics Sichuan University  Chengdu China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2024,7,15]]},"reference":[{"volume-title":"Set Theory On the Structure of the Real Line","year":"1995","author":"Bartoszynski T.","key":"e_1_2_7_2_1"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2019.01.015"},{"issue":"3","key":"e_1_2_7_4_1","first-page":"355","article-title":"Some observations on filters with properties defined by open covers","volume":"56","author":"Hern\u00e1ndez\u2010Guti\u00e9rrez R.","year":"2015","journal-title":"Comment. 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