{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T09:08:27Z","timestamp":1649063307397},"reference-count":2,"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":6401,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1996,9]]},"abstract":"<jats:p>It is well known that every Boolean algebra of size <jats:italic>\u03c9<\/jats:italic><jats:sub>1<\/jats:sub> can be embedded into <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200017163_inline1\" \/>(<jats:italic>\u03c9<\/jats:italic>)\/fin. E. van Douwen proved that if CH failed then there is a Boolean algebra of size <jats:italic>\u03c9<\/jats:italic><jats:sub>2<\/jats:sub> which cannot be embedded into <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200017163_inline1\" \/>(<jats:italic>\u03c9<\/jats:italic><jats:sub>1<\/jats:sub>)\/ctble. We show that \u25c7 is equivalent to the statement that a certain natural Boolean algebra of size <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200017163_inline2\" \/> embeds into <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200017163_inline1\" \/>(<jats:italic>\u03c9<\/jats:italic><jats:sub>1<\/jats:sub>)\/ctble. I would like to thank B. Velickovic for many helpful conversations.<\/jats:p>","DOI":"10.2307\/2275789","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:59:03Z","timestamp":1146941943000},"page":"873-879","source":"Crossref","is-referenced-by-count":0,"title":["On boolean subalgebras of  (<i>\u03c9<\/i><sub>1<\/sub>)\/ctble"],"prefix":"10.1017","volume":"61","author":[{"given":"Alan","family":"Dow","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200017163_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0166-8641(91)90073-U"},{"key":"S0022481200017163_ref001","volume-title":"Axiomatic set theory","author":"Shelah","year":"1984"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200017163","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T16:33:44Z","timestamp":1557678824000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200017163\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,9]]},"references-count":2,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1996,9]]}},"alternative-id":["S0022481200017163"],"URL":"https:\/\/doi.org\/10.2307\/2275789","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,9]]}}}