{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T14:17:15Z","timestamp":1773152235095,"version":"3.50.1"},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4667,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2001,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The Mycielski ideal<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200010951_inline1\"\/>is defined to consist of all sets<jats:italic>A<\/jats:italic>\u2286<jats:sup>\u2115<\/jats:sup><jats:italic>k<\/jats:italic>such that {<jats:italic>f<\/jats:italic>\u21be<jats:italic>X<\/jats:italic>:<jats:italic>f<\/jats:italic>\u2208<jats:italic>A<\/jats:italic>} \u2260<jats:italic><jats:sup>X<\/jats:sup>k<\/jats:italic>for all<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200010951_inline2\"\/>. It will be shown that the covering numbers for these ideals are all equal. However, the covering numbers of the closely associated Ros\u0142anowski ideals will be shown to be consistently different.<\/jats:p>","DOI":"10.2307\/2695039","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:05:52Z","timestamp":1146938752000},"page":"707-718","source":"Crossref","is-referenced-by-count":5,"title":["The covering numbers of Mycielski ideals are all equal"],"prefix":"10.1017","volume":"66","author":[{"given":"Saharon","family":"Shelah","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juris","family":"Stepr\u0101ns","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200010951_ref005","doi-asserted-by":"publisher","DOI":"10.4064\/cm-65-2-291-299"},{"key":"S0022481200010951_ref006","doi-asserted-by":"publisher","DOI":"10.4064\/cm-20-1-71-76"},{"key":"S0022481200010951_ref008","doi-asserted-by":"publisher","DOI":"10.4064\/cm-66-2-187-200"},{"key":"S0022481200010951_ref009","doi-asserted-by":"publisher","DOI":"10.4064\/cm-59-2-159-168"},{"key":"S0022481200010951_ref001","doi-asserted-by":"crossref","first-page":"532","DOI":"10.2307\/44152299","article-title":"Typical properties of continuous functions via the Vietoris topology","volume":"18","author":"Balcerzak","year":"1992","journal-title":"Real Analysis Exchange"},{"key":"S0022481200010951_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1990-1007486-6"},{"key":"S0022481200010951_ref003","first-page":"42","volume":"58","author":"Cicho\u0144","year":"1993","journal-title":"Combinatorial properties of the ideal \u01a52"},{"key":"S0022481200010951_ref004","doi-asserted-by":"publisher","DOI":"10.1515\/dema-1989-0105"},{"key":"S0022481200010951_ref007","doi-asserted-by":"publisher","DOI":"10.4064\/cm-69-2-297-298"},{"key":"S0022481200010951_ref011","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1305\/ndjfl\/1040511341","article-title":"Uniformization problems and the cofinalily of the infinite symmetric group","volume":"35","author":"Sharp","year":"1994","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S0022481200010951_ref010","doi-asserted-by":"crossref","first-page":"98","DOI":"10.2307\/44153817","article-title":"A category base for Mycielski's ideals","volume":"19","author":"Schilling","year":"1993","journal-title":"Real Analysis Exchange"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200010951","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,14]],"date-time":"2020-04-14T14:14:02Z","timestamp":1586873642000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200010951\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,6]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2001,6]]}},"alternative-id":["S0022481200010951"],"URL":"https:\/\/doi.org\/10.2307\/2695039","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,6]]}}}