{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T15:29:05Z","timestamp":1759073345428},"reference-count":16,"publisher":"Wiley","issue":"4-5","license":[{"start":{"date-parts":[[2013,8,5]],"date-time":"2013-08-05T00:00:00Z","timestamp":1375660800000},"content-version":"vor","delay-in-days":4,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2013,8]]},"abstract":"Let X<\/jats:italic> be an infinite set and let and denote the propositions \u201cevery filter on<\/jats:italic> X<\/jats:italic> can be extended to an ultrafilter<\/jats:italic>\u201d and \u201cX<\/jats:italic> has a free ultrafilter<\/jats:italic>\u201d, respectively. We denote by the Stone space<\/jats:italic> of the Boolean algebra of all subsets of X<\/jats:italic>. We show:\n\nFor every well\u2010ordered cardinal number \u2135, (\u2135) iff (2\u2135<\/jats:sup>).<\/jats:p><\/jats:list-item>\n iff \u201c is a continuous image of<\/jats:italic> \u201d iff \u201c has a free open ultrafilter<\/jats:italic>\n\u201d iff \u201cevery countably infinite subset of<\/jats:italic> has a limit point<\/jats:italic>\u201d.<\/jats:p><\/jats:list-item>\n implies \u201cevery open filter on<\/jats:italic> extends to an open ultrafilter<\/jats:italic>\u201d implies \u201chas an open ultrafilter<\/jats:italic>\u201d implies <\/jats:p><\/jats:list-item>\nIt is relatively consistent with that (\u03c9) holds, whereas (\u03c9) fails. In particular, none of the statements given in (2) implies (\u03c9).<\/jats:p><\/jats:list-item>\n<\/jats:list>\n<\/jats:p>","DOI":"10.1002\/malq.201100092","type":"journal-article","created":{"date-parts":[[2013,8,5]],"date-time":"2013-08-05T09:36:53Z","timestamp":1375695413000},"page":"258-267","source":"Crossref","is-referenced-by-count":8,"title":["The existence of free ultrafilters on \u03c9 does not imply the extension of filters on \u03c9 to ultrafilters"],"prefix":"10.1002","volume":"59","author":[{"given":"Eric J.","family":"Hall","sequence":"first","affiliation":[{"name":"Department of Mathematics & Statistics University of Missouri\u2014Kansas City 206 Haag Hall, 5100 Rockhill Rd Kansas City MO 64110 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kyriakos","family":"Keremedis","sequence":"additional","affiliation":[{"name":"Department of Mathematics University of the Aegean Karlovassi Samos 83200 Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eleftherios","family":"Tachtsis","sequence":"additional","affiliation":[{"name":"Department of Mathematics University of the Aegean Karlovassi Samos 83200 Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2013,8,5]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.2307\/2273223"},{"key":"e_1_2_7_3_1","doi-asserted-by":"crossref","unstructured":"M.\u00a0R.Burke Liftings for noncomplete probability spaces in:Papers on general topology and applications. Papers from the Seventh Summer Conference in honor of Mary Ellen Rudin held at the University of Wisconsin Madison Wisconsin June 26\u201329 1991 edited byS.Andima R.Kopperman P. R.Misra M. E.RudinandA. R.Todd Annals of the New York Academy of Sciences Vol. 704 (New York Academy of Sciences New York) pp.34\u201337.","DOI":"10.1111\/j.1749-6632.1993.tb52507.x"},{"key":"e_1_2_7_4_1","volume-title":"Lecture Notes in Mathematics","author":"Felgner U.","year":"1971"},{"key":"e_1_2_7_5_1","first-page":"111","article-title":"\u010cech\u2010stone compactifications of discrete spaces and restricted forms of the boolean prime ideal theorem","volume":"41","author":"Hall E.\u00a0J.","year":"2013","journal-title":"Topology Proc."},{"key":"e_1_2_7_6_1","volume-title":"Axiom of choice, Lecture Notes in Mathematics","author":"Herrlich H.","year":"2006"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00124110"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.4064\/ba59-2-1"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/059"},{"key":"e_1_2_7_10_1","volume-title":"The axiom of choice","author":"Jech T.\u00a0J.","year":"1973"},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.4064\/ba53-4-1"},{"key":"e_1_2_7_12_1","doi-asserted-by":"publisher","DOI":"10.4064\/ba55-4-1"},{"key":"e_1_2_7_13_1","first-page":"15","article-title":"Extensions of compactness of Tychonoff powers of 2 in ZF","volume":"37","author":"Keremedis K.","year":"2011","journal-title":"Topology Proc."},{"key":"e_1_2_7_14_1","doi-asserted-by":"publisher","DOI":"10.2307\/2273318"},{"issue":"4","key":"e_1_2_7_15_1","first-page":"313","article-title":"The Boolean prime ideal theorem holds iff maximal open filters exist","volume":"43","author":"Rhineghost Y.\u00a0T.","year":"2002","journal-title":"Cah. Topol. G\u00e9om. Diff\u00e9r. Cat\u00e9g."},{"key":"e_1_2_7_16_1","doi-asserted-by":"publisher","DOI":"10.1002\/mana.19770790112"},{"key":"e_1_2_7_17_1","doi-asserted-by":"publisher","DOI":"10.4064\/ba58-2-1"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201100092","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201100092","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201100092","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T02:05:51Z","timestamp":1696385151000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201100092"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8]]},"references-count":16,"journal-issue":{"issue":"4-5","published-print":{"date-parts":[[2013,8]]}},"alternative-id":["10.1002\/malq.201100092"],"URL":"https:\/\/doi.org\/10.1002\/malq.201100092","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,8]]}}}