{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T15:25:11Z","timestamp":1759073111612,"version":"3.37.3"},"reference-count":7,"publisher":"Wiley","issue":"1-2","license":[{"start":{"date-parts":[[2014,2,4]],"date-time":"2014-02-04T00:00:00Z","timestamp":1391472000000},"content-version":"vor","delay-in-days":3,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"name":"NSF","award":["DMS 1161078"],"award-info":[{"award-number":["DMS 1161078"]}]},{"name":"Institutional Research Plan","award":["AV0Z10190503","IAA100190902"],"award-info":[{"award-number":["AV0Z10190503","IAA100190902"]}]},{"DOI":"10.13039\/501100010188","name":"COCyTECH","doi-asserted-by":"crossref","award":["CHIS-2006-C06-457770"],"award-info":[{"award-number":["CHIS-2006-C06-457770"]}],"id":[{"id":"10.13039\/501100010188","id-type":"DOI","asserted-by":"crossref"}]},{"name":"PROMEP","award":["UNACH-PTC-073","SIINV-UNACH"],"award-info":[{"award-number":["UNACH-PTC-073","SIINV-UNACH"]}]},{"DOI":"10.13039\/501100001824","name":"GA \u010cR","doi-asserted-by":"crossref","award":["201-03-0933"],"award-info":[{"award-number":["201-03-0933"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"crossref"}]},{"name":"PAPIIT","award":["IN101608","IN102311"],"award-info":[{"award-number":["IN101608","IN102311"]}]},{"name":"CONACYT","award":["80355"],"award-info":[{"award-number":["80355"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2014,2]]},"abstract":"<jats:p>We study the possible values of the cofinality invariant for various Borel ideals on the natural numbers. We introduce the notions of a fragmented and gradually fragmented <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200079-math-0001.png\" xlink:title=\"urn:x-wiley:09425616:malq201200079:equation:malq201200079-math-0001\"\/> ideal and prove a dichotomy for fragmented ideals. We show that every gradually fragmented ideal has cofinality consistently strictly smaller than the cardinal invariant <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201200079-math-0002.png\" xlink:title=\"urn:x-wiley:09425616:malq201200079:equation:malq201200079-math-0002\"\/> and produce a model where there are uncountably many pairwise distinct cofinalities of gradually fragmented ideals.<\/jats:p>","DOI":"10.1002\/malq.201200079","type":"journal-article","created":{"date-parts":[[2014,2,4]],"date-time":"2014-02-04T22:28:18Z","timestamp":1391552898000},"page":"31-39","source":"Crossref","is-referenced-by-count":3,"title":["Cofinalities of Borel ideals"],"prefix":"10.1002","volume":"60","author":[{"given":"Michael","family":"Hru\u0161\u00e1k","sequence":"first","affiliation":[{"name":"Centro de Ciencias Matem\u00e1ticas Universidad Nacional Aut\u00f3noma de M\u00e9xico, Campus Morelia Apartado Postal 611\u20103 (Xangari)  C.P. 58089 Morelia Michoac\u00e1n M\u00e9xico"},{"name":"Institute of Mathematics Academy of Sciences of the Czech Republic  \u017ditn\u00e1 25, 115 67, Praha 1 Czech Republic"}]},{"given":"Diego","family":"Rojas\u2010Rebolledo","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computing Science Saint Mary's University  923 Robie Street, Halifax, NS, B3H 3C3 Canada"}]},{"given":"Jind\u0159ich","family":"Zapletal","sequence":"additional","affiliation":[{"name":"Institute of Mathematics Academy of Sciences of the Czech Republic  \u017ditn\u00e1 25, 115 67, Praha 1 Czech Republic"},{"name":"Department of Mathematics University of Florida  358 Little Hall P. O. Box 118105 Gainesville FL 32611\u20108105 United States of America"}]}],"member":"311","published-online":{"date-parts":[[2014,2,4]]},"reference":[{"key":"e_1_2_5_2_1","doi-asserted-by":"publisher","DOI":"10.1201\/9781439863466"},{"key":"e_1_2_5_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01375552"},{"key":"e_1_2_5_4_1","first-page":"26","volume-title":"Set theory and its applications, edited by L. Babinkostova, A. E. Caicedo, S. Geschke, and M. Scheepers, Contemporary Mathematics","author":"Hru\u0161\u00e1k M.","year":"2011"},{"key":"e_1_2_5_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(98)00065-7"},{"key":"e_1_2_5_6_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-00-05061-9"},{"volume-title":"Memoirs of the American Mathematical Society","year":"1999","author":"Roslanowski A.","key":"e_1_2_5_7_1"},{"volume-title":"Cambridge Tracts in Mathematics","year":"2008","author":"Zapletal J.","key":"e_1_2_5_8_1"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201200079","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201200079","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201200079","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,5]],"date-time":"2023-10-05T03:59:45Z","timestamp":1696478385000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201200079"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,2]]},"references-count":7,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2014,2]]}},"alternative-id":["10.1002\/malq.201200079"],"URL":"https:\/\/doi.org\/10.1002\/malq.201200079","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"type":"print","value":"0942-5616"},{"type":"electronic","value":"1521-3870"}],"subject":[],"published":{"date-parts":[[2014,2]]}}}