{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T17:18:30Z","timestamp":1773249510308,"version":"3.50.1"},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4759,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2001,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A maximal almost disjoint (mad) family <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200011300_inline1\"\/> \u2286 [<jats:italic>\u03c9<\/jats:italic>]<jats:sup><jats:italic>\u03c9<\/jats:italic><\/jats:sup> is Cohen-stable if and only if it remains maximal in any Cohen generic extension. Otherwise it is Cohen-unstable. It is shown that a mad family. <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200011300_inline1\"\/>.is Cohen-unstable if and only if there is a bijection <jats:italic>G<\/jats:italic> from <jats:italic>\u03c9<\/jats:italic> to the rationals such that the sets <jats:italic>G<\/jats:italic>[<jats:italic>A<\/jats:italic>]. <jats:italic>A<\/jats:italic> \u2208 <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200011300_inline1\"\/> are nowhere dense. An \u2135<jats:sub>0<\/jats:sub>-mad family, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200011300_inline1\"\/>. is a mad family with the property that given any countable family \u212c \u2282 [<jats:italic>\u03c9<\/jats:italic>]<jats:sup><jats:italic>\u03c9<\/jats:italic><\/jats:sup> such that each element of \u212c meets infinitely many elements of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200011300_inline1\"\/> in an infinite set there is an element of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200011300_inline1\"\/> meeting each element of \u212c in an infinite set. It is shown that Cohen-stable mad families exist if and only if there exist \u2135<jats:sub>0<\/jats:sub>-mad families. Either of the conditions b = c or a &lt; cov(<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200011300_inline2\"\/>) implies that there exist Cohen-stable mad families. Similar results are obtained for splitting families. For example, a splitting family. <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200011300_inline3\"\/>. is Cohen-unstable if and only if there is a bijection <jats:italic>G<\/jats:italic> from <jats:italic>\u03c9<\/jats:italic> to the rationals such that the boundaries of the sets <jats:italic>G<\/jats:italic>[<jats:italic>S<\/jats:italic>], <jats:italic>S<\/jats:italic> \u2208 <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200011300_inline3\"\/> are nowhere dense. Also. Cohen-stable splitting families of cardinality \u2264 <jats:italic>\u03ba<\/jats:italic> exist if and only if \u2135<jats:sub>0<\/jats:sub>-splitting families of cardinality \u2264 <jats:italic>\u03ba<\/jats:italic> exist.<\/jats:p>","DOI":"10.2307\/2694920","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:03:53Z","timestamp":1146938633000},"page":"257-270","source":"Crossref","is-referenced-by-count":19,"title":["Cohen-stable families of subsets of integers"],"prefix":"10.1017","volume":"66","author":[{"given":"Milo\u0161 S.","family":"Kurili\u0107","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200011300_ref006","doi-asserted-by":"publisher","DOI":"10.2307\/1970696"},{"key":"S0022481200011300_ref003","volume-title":"Set theory, an introduction to independence proofs","author":"Kunen","year":"1980"},{"key":"S0022481200011300_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0016-660X(72)90001-3"},{"key":"S0022481200011300_ref008","first-page":"195","volume-title":"Open problems in topology","author":"Vaughan","year":"1990"},{"key":"S0022481200011300_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/s001530050044"},{"key":"S0022481200011300_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-444-86580-9.50023-9"},{"key":"S0022481200011300_ref005","first-page":"1","article-title":"Topological properties of Cohen generic extensions","volume":"52","author":"Malyhin","year":"1990","journal-title":"Transactions of the Moscow Mathematical Society"},{"key":"S0022481200011300_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-444-86580-9.50006-9"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200011300","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,8]],"date-time":"2019-05-08T00:46:14Z","timestamp":1557276374000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200011300\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,3]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2001,3]]}},"alternative-id":["S0022481200011300"],"URL":"https:\/\/doi.org\/10.2307\/2694920","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,3]]}}}