{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T18:59:50Z","timestamp":1758394790518},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":5671,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1998,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>P<\/jats:italic> be any one of the following combinatorial properties: weak <jats:italic>P<\/jats:italic>-pointness, weak (semi-) <jats:italic>Q<\/jats:italic>-pointness, weak (semi-)selectivity, \u03c9-closedness. We deal with the following two questions: (1) What is the least cardinal <jats:italic>k<\/jats:italic> such that there exists an ideal with <jats:italic>k<\/jats:italic> many generators that does not have the property <jats:italic>P<\/jats:italic>? (2) Can one extend every ideal with the property <jats:italic>P<\/jats:italic> to a prime ideal with the property <jats:italic>P<\/jats:italic>?<\/jats:p>","DOI":"10.2307\/2586725","type":"journal-article","created":{"date-parts":[[2006,11,18]],"date-time":"2006-11-18T09:42:09Z","timestamp":1163842929000},"page":"1040-1054","source":"Crossref","is-referenced-by-count":7,"title":["Ideals over \u03c9 and cardinal invariants of the continuum"],"prefix":"10.1017","volume":"63","author":[{"given":"P.","family":"Matet","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Pawlikowski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200014729_ref012","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1985-0776210-2"},{"key":"S0022481200014729_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-9754-0_14"},{"key":"S0022481200014729_ref010","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1981-0613787-2"},{"key":"S0022481200014729_ref014","first-page":"357","volume-title":"Set theory","volume":"26","author":"Shelah","year":"1992"},{"key":"S0022481200014729_ref015","first-page":"195","volume-title":"Open problems in topology","author":"Vaughan","year":"1990"},{"key":"S0022481200014729_ref004","doi-asserted-by":"crossref","DOI":"10.1201\/9781439863466","volume-title":"Set theory: On the structure of the real line","author":"Bartoszy\u0144ski","year":"1995"},{"key":"S0022481200014729_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(71)90011-8"},{"key":"S0022481200014729_ref013","unstructured":"Ros\u0142anowski A. and Shelah S. , Norms on possibilities I: a missing chapter of [Sh.f], preprint."},{"key":"S0022481200014729_ref007","first-page":"1323","volume":"58","author":"Goldstern","year":"1993","journal-title":"Strong measure zero sets without Cohen reals"},{"key":"S0022481200014729_ref001","doi-asserted-by":"crossref","first-page":"225","DOI":"10.4064\/fm-127-3-225-239","article-title":"Combinatorial aspects of measure and category","volume":"127","author":"Bartoszy\u0144ski","year":"1987","journal-title":"Fundamenta Mathematicae"},{"key":"S0022481200014729_ref002","first-page":"828","volume":"54","author":"Bartoszy\u0144ski","year":"1989","journal-title":"On the cofinality of the smallest covering of the real line by meager sets"},{"key":"S0022481200014729_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1990-0993747-3"},{"key":"S0022481200014729_ref006","first-page":"A","article-title":"Strong measure zero sets","volume":"26","author":"Galvin","year":"1979","journal-title":"Notices of the American Mathematical Society"},{"key":"S0022481200014729_ref009","doi-asserted-by":"crossref","first-page":"91","DOI":"10.4064\/fm-92-2-91-94","article-title":"On the existence of P-points in the Stone-\u010cech compactification of integers","volume":"92","author":"Ketonen","year":"1976","journal-title":"Fundamenta Mathematicae"},{"key":"S0022481200014729_ref011","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1984-0735576-9"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200014729","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T20:21:09Z","timestamp":1557519669000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200014729\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,9]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1998,9]]}},"alternative-id":["S0022481200014729"],"URL":"https:\/\/doi.org\/10.2307\/2586725","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,9]]}}}