{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T15:38:16Z","timestamp":1759073896578},"reference-count":25,"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>Using a dictionary translating a variety of classical and modern covering properties into combinatorial properties of continuous images, we get a simple way to understand the interrelations between these properties in ZFC and in the realm of the trichotomy axiom for upward closed families of sets of natural numbers. While it is now known that the answer to the Hurewicz 1927 problem is positive, it is shown here that semifilter trichotomy implies a negative answer to a slightly stronger form of this problem.<\/jats:p>","DOI":"10.2178\/jsl\/1230396918","type":"journal-article","created":{"date-parts":[[2008,12,27]],"date-time":"2008-12-27T11:55:26Z","timestamp":1230378926000},"page":"1278-1288","source":"Crossref","is-referenced-by-count":7,"title":["Combinatorial images of sets of reals and semifilter trichotomy"],"prefix":"10.1017","volume":"73","author":[{"given":"Boaz","family":"Tsaban","sequence":"first","affiliation":[]},{"given":"Lyubomyr","family":"Zdomskyy","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200003996_ref014","doi-asserted-by":"publisher","DOI":"10.4064\/fm-144-1-43-54"},{"key":"S0022481200003996_ref005","first-page":"50","volume":"54","author":"Blass","year":"1989","journal-title":"Consistency results about filters and the number of inequivalent growth types"},{"key":"S0022481200003996_ref019","doi-asserted-by":"publisher","DOI":"10.14321\/realanalexch.27.2.0757"},{"key":"S0022481200003996_ref023","first-page":"1053","volume":"71","author":"Tsaban","year":"2006","journal-title":"Menger's covering property and groupwise density"},{"key":"S0022481200003996_ref022","first-page":"245","volume-title":"Selection Principles and Covering Properties in Topology","volume":"18","author":"Tsaban","year":"2007"},{"key":"S0022481200003996_ref018","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-8641(01)00078-5"},{"key":"S0022481200003996_ref021","doi-asserted-by":"publisher","DOI":"10.4064\/fm181-3-5"},{"key":"S0022481200003996_ref012","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1992-1028761-1"},{"key":"S0022481200003996_ref015","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2005.11.012"},{"key":"S0022481200003996_ref013","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2005.09.008"},{"key":"S0022481200003996_ref001","volume-title":"Coherence of semifilters","author":"Banakh"},{"key":"S0022481200003996_ref002","first-page":"1254","volume":"68","author":"Bartoszy\u0144ski","year":"2003","journal-title":"Additivity properties of topological diagonalizations"},{"key":"S0022481200003996_ref003","volume-title":"Handbook of Set Theory","author":"Blass"},{"key":"S0022481200003996_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF01793782"},{"key":"S0022481200003996_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(87)90082-0"},{"key":"S0022481200003996_ref007","unstructured":"Chaber J. and Pol R. , A remark on Fremlin-Miller theorem concerning the Menger property and Michael concentrated sets, unpublished note (10 2002)."},{"key":"S0022481200003996_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0166-8641(84)90038-5"},{"key":"S0022481200003996_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0166-8641(82)90065-7"},{"key":"S0022481200003996_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-8641(96)00075-2"},{"key":"S0022481200003996_ref011","doi-asserted-by":"publisher","DOI":"10.4064\/fm179-2-2"},{"key":"S0022481200003996_ref016","volume-title":"Topology and its Applications","author":"Samet"},{"key":"S0022481200003996_ref017","doi-asserted-by":"publisher","DOI":"10.1016\/0166-8641(95)00067-4"},{"key":"S0022481200003996_ref020","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2003.03.001"},{"key":"S0022481200003996_ref024","doi-asserted-by":"publisher","DOI":"10.4171\/JEMS\/132"},{"key":"S0022481200003996_ref025","first-page":"525","article-title":"A semifilter approach to selection principles","volume":"46","author":"Zdomskyy","year":"2005","journal-title":"Commentationes Mathematicae Universitatis Carolinae"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200003996","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,30]],"date-time":"2019-04-30T17:36:30Z","timestamp":1556645790000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200003996\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,12]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,12]]}},"alternative-id":["S0022481200003996"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1230396918","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,12]]}}}