{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T21:46:13Z","timestamp":1773265573499,"version":"3.50.1"},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":101,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2013,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove the consistency of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200126477_inline01\"\/> together with the existence of a <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200126477_inline02\"\/>-definable mad family, answering a question posed by Friedman and Zdomskyy in [7, Question 16]. For the proof we construct a mad family in <jats:italic>L<\/jats:italic> which is an \u2135<jats:sub>1<\/jats:sub>-union of perfect a.d. sets, such that this union remains mad in the iterated Hechler extension. The construction also leads us to isolate a new cardinal invariant, the <jats:italic>Borel almost-disjointness number<\/jats:italic><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200126477_inline03\"\/>, defined as the least number of Borel a.d. sets whose union is a mad family. Our proof yields the consistency of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200126477_inline04\"\/> (and hence, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200126477_inline05\"\/>).<\/jats:p>","DOI":"10.2178\/jsl.7804070","type":"journal-article","created":{"date-parts":[[2014,1,5]],"date-time":"2014-01-05T15:33:25Z","timestamp":1388936005000},"page":"1164-1180","source":"Crossref","is-referenced-by-count":9,"title":["Mad Families Constructed from Perfect Almost Disjoint Families"],"prefix":"10.1017","volume":"78","author":[{"given":"J\u00f6rg","family":"Brendle","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yurii","family":"Khomskii","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200126477_ref001","first-page":"94","volume":"50","author":"Baumgartner","year":"1985","journal-title":"Adjoining dominating functions"},{"key":"S0022481200126477_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2011.04.001"},{"key":"S0022481200126477_ref002","volume-title":"Forcing and the structure of the real line: the Bogot\u00e1 lectures","author":"Brendle","year":"2009"},{"key":"S0022481200126477_ref015","first-page":"1181","volume":"78","author":"T\u00f2rnquist","year":"2013","journal-title":"\u03a32\n                  1 and \u03a01\n                  1 mad families"},{"key":"S0022481200126477_ref003","volume-title":"Aspects of iterated forcing","author":"Brendle","year":"2010"},{"key":"S0022481200126477_ref014","doi-asserted-by":"publisher","DOI":"10.4064\/fm217-1-6"},{"key":"S0022481200126477_ref005","first-page":"241","article-title":"Two classes of Fr\u00e9chet-Urysohn spaces","volume":"108","author":"Dow","year":"1990","journal-title":"Proceedings of the American Mathematical Society"},{"key":"S0022481200126477_ref011","first-page":"59","article-title":"Happy families","volume":"12","author":"Mathias","year":"1977","journal-title":"Annals of Pure and Applied Logic"},{"key":"S0022481200126477_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2004.09.002"},{"key":"S0022481200126477_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2010.06.007"},{"key":"S0022481200126477_ref008","first-page":"345","article-title":"MAD families and the rationals","volume":"42","author":"Hrusak","year":"2001","journal-title":"Commentationes Mathematicae Universitatis Carolinae"},{"key":"S0022481200126477_ref009","first-page":"1158","volume":"73","author":"Kastermans","year":"2008","journal-title":"Analytic and coanalytic families of almost disjoint functions"},{"key":"S0022481200126477_ref010","first-page":"257","volume":"66","author":"Kurili\u0107","year":"2001","journal-title":"Cohen-stable families of subsets of integers"},{"key":"S0022481200126477_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(89)90013-4"},{"key":"S0022481200126477_ref013","doi-asserted-by":"publisher","DOI":"10.4064\/fm204-3-3"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200126477","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,22]],"date-time":"2019-04-22T22:19:31Z","timestamp":1555971571000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200126477\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12]]},"references-count":15,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2013,12]]}},"alternative-id":["S0022481200126477"],"URL":"https:\/\/doi.org\/10.2178\/jsl.7804070","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12]]}}}