{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T10:19:56Z","timestamp":1773397196512,"version":"3.50.1"},"reference-count":11,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2003,1,21]],"date-time":"2003-01-21T00:00:00Z","timestamp":1043107200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2003,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For <jats:italic>a<\/jats:italic> \u2286 <jats:italic>b<\/jats:italic> \u2286 <jats:italic>\u03c9<\/jats:italic> with  <jats:italic>b<\/jats:italic>\\ <jats:italic>a<\/jats:italic> infinite, the set <jats:italic>D<\/jats:italic> = {<jats:italic>x<\/jats:italic> \u2208 [<jats:italic>\u03c9<\/jats:italic>]<jats:sup><jats:italic>\u03c9<\/jats:italic><\/jats:sup> : <jats:italic>a<\/jats:italic> \u2286 <jats:italic>x<\/jats:italic> \u2286 <jats:italic>b<\/jats:italic>} is called a <jats:italic>doughnut<\/jats:italic>. A set <jats:italic>S<\/jats:italic> \u2286 [<jats:italic>\u03c9<\/jats:italic>]<jats:sup><jats:italic>\u03c9<\/jats:italic><\/jats:sup> has the doughnut property \ud835\udc9f if it contains or is disjoint from a doughnut. It is known that not every set <jats:italic>S<\/jats:italic> \u2286 [<jats:italic>\u03c9<\/jats:italic>]<jats:sup><jats:italic>\u03c9<\/jats:italic><\/jats:sup> has the doughnut property, but <jats:italic>S<\/jats:italic> has the doughnut property if it has the Baire property \u212c\ufe01 or the Ramsey property \u211b. In this paper it is shown that a finite support iteration of length <jats:italic>\u03c9<\/jats:italic><jats:sub>1<\/jats:sub> of Cohen forcing, starting from <jats:bold><jats:italic>L<\/jats:italic><\/jats:bold>, yields a model for CH + <jats:styled-content>$ \\sum ^1 _2 $<\/jats:styled-content>(\ud835\udc9f) + <jats:styled-content>$ \\neg \\sum ^1 _2 $<\/jats:styled-content>(\u212c\ufe01) + <jats:styled-content>$ \\neg \\sum ^1 _2 $<\/jats:styled-content>(\u211b).<\/jats:p>","DOI":"10.1002\/malq.200310016","type":"journal-article","created":{"date-parts":[[2003,1,24]],"date-time":"2003-01-24T16:13:50Z","timestamp":1043424830000},"page":"173-178","source":"Crossref","is-referenced-by-count":11,"title":["Making doughnuts of Cohen reals"],"prefix":"10.1002","volume":"49","author":[{"given":"Lorenz","family":"Halbeisen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2003,1,21]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"T.Bartoszy\u0144skiandH.Judah Set Theory: On the Structure of the Real Line (A. 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