{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,30]],"date-time":"2023-10-30T06:43:55Z","timestamp":1698648235666},"reference-count":16,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2010,11,17]],"date-time":"2010-11-17T00:00:00Z","timestamp":1289952000000},"content-version":"vor","delay-in-days":4338,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1999,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We find topological characterizations of the pseudointersection number \ud835\udd2d and the tower number t of the real line and we show that \ud835\udd2d &lt; <jats:italic>t<\/jats:italic> iff there exists a compact separable T<jats:sub>2<\/jats:sub> space <jats:italic>X<\/jats:italic> of \u03c0\u2010weight &lt; \ud835\udd2d that can be covered by &lt; <jats:italic>t<\/jats:italic> nowhere dense sets iff there exists a weak Hausdorff gap of size <jats:italic>K<\/jats:italic> &lt; t, i. e., a pair ({<jats:italic>A<\/jats:italic> : i \u2260 <jats:italic>k<\/jats:italic>}, {<jats:italic>B<\/jats:italic><jats:sub>J<\/jats:sub> : j \u03b5 <jats:italic>K<\/jats:italic>}) C [W]<jats:sup>W<\/jats:sup> X [<jats:italic>U<\/jats:italic>]<jats:italic>W<\/jats:italic> such that <jats:italic>A<\/jats:italic> = {<jats:italic>A<\/jats:italic><jats:sub>i<\/jats:sub> : i \u03b5 K} is a decreasing tower, <jats:italic>B<\/jats:italic> = {<jats:italic>B<\/jats:italic><jats:sub>j<\/jats:sub> : j \u03b5 <jats:italic>K<\/jats:italic>) is a family of pseudointersections of <jats:italic>A<\/jats:italic>, and there is no pseudointersection <jats:italic>S<\/jats:italic> of <jats:italic>A<\/jats:italic> meeting each member of <jats:italic>B<\/jats:italic> in an infinite set.<\/jats:p>","DOI":"10.1002\/malq.19990450109","type":"journal-article","created":{"date-parts":[[2010,11,17]],"date-time":"2010-11-17T16:27:15Z","timestamp":1290011235000},"page":"95-104","source":"Crossref","is-referenced-by-count":0,"title":["Weak Hausdorff Gaps and the \ud835\udd2d \u2264 <i>t<\/i> Problem"],"prefix":"10.1002","volume":"45","author":[{"given":"Kyriakos","family":"Keremedis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2010,11,17]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","first-page":"149","DOI":"10.4064\/fm-114-2-149-157","article-title":"On the combinatorial principle P(c)","author":"Bell M. 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