{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T15:26:53Z","timestamp":1773242813889,"version":"3.50.1"},"reference-count":7,"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":5490,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1999,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that every analytic set in <jats:sup>\u03c9<\/jats:sup>\u03c9 \u00d7 <jats:sup>\u03c9<\/jats:sup>\u03c9 with \u03c3-bounded sections has a not \u03c3-bounded closed free set. We show that this result is sharp. There exists a closed set with bounded sections which has no dominating analytic free set. and there exists a closed set with non-dominating sections which does not have a not \u03c3-bounded analytic free set. Under projective determinacy analytic can be replaced in the above results by projective.<\/jats:p>","DOI":"10.2307\/2586752","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:02:25Z","timestamp":1146938545000},"page":"75-80","source":"Crossref","is-referenced-by-count":6,"title":["Dominating and unbounded free sets"],"prefix":"10.1017","volume":"64","author":[{"given":"Slawomir","family":"Solecki","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Otmar","family":"Spinas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200013918_ref004","doi-asserted-by":"crossref","first-page":"165\u2013169","DOI":"10.4064\/fm-61-2-165-169","article-title":"Algebraic independence and measure","volume":"61","author":"Mycielski","year":"1967","journal-title":"Fundamenta Mathematicae"},{"key":"S0022481200013918_ref003","first-page":"139\u2013147","article-title":"Independent sets in topological algebras","volume":"55","author":"Mycielski","year":"1964","journal-title":"Fandamenta Mathematicae"},{"key":"S0022481200013918_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1977-0450070-1"},{"key":"S0022481200013918_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1987-0884475-3"},{"key":"S0022481200013918_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4190-4"},{"key":"S0022481200013918_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)90025-6"},{"key":"S0022481200013918_ref006","first-page":"85\u201387","article-title":"Approximation des sous-ensembles analytiques par l\u2019int\u00e9rieur","volume":"281","author":"Raymond","year":"1975","journal-title":"Comptes Rendus l\u2019 Acad\u00e9mie des Science Paris, S\u00e9rie A"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200013918","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T19:06:42Z","timestamp":1557515202000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200013918\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,3]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1999,3]]}},"alternative-id":["S0022481200013918"],"URL":"https:\/\/doi.org\/10.2307\/2586752","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,3]]}}}