{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T02:30:44Z","timestamp":1776997844124,"version":"3.51.4"},"reference-count":12,"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":1927,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2008,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>If<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200003923_inline1\"\/>is an analytic family of pairwise eventually different functions then the following strong maximality condition fails: For any countable<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200003923_inline2\"\/>, no member of which is covered by finitely many functions from<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200003923_inline3\"\/>, there is<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200003923_inline4\"\/>such that for all<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200003923_inline5\"\/>there are infinitely many integers<jats:italic>k<\/jats:italic>such that<jats:italic>f(k) = h(k)<\/jats:italic>. However if<jats:italic>V = L<\/jats:italic>then there exists a coanalytic family of pairwise eventually different functions satisfying this strong maximality condition.<\/jats:p>","DOI":"10.2178\/jsl\/1230396911","type":"journal-article","created":{"date-parts":[[2008,12,27]],"date-time":"2008-12-27T16:55:26Z","timestamp":1230396926000},"page":"1158-1172","source":"Crossref","is-referenced-by-count":5,"title":["Analytic and coanalytic families of almost disjoint functions"],"prefix":"10.1017","volume":"73","author":[{"given":"Bart","family":"Kastermans","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"family":"Juris Stepr\u0101ns","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200003923_ref006","volume-title":"Set theory. 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