{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T23:02:58Z","timestamp":1648681378618},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4759,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2001,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce a new cardinal characteristic r*. related to the reaping number r. and show that<\/jats:p><jats:p>\u2022 posets of size &lt; <jats:italic>r<\/jats:italic>* which add reals add unbounded reals;<\/jats:p><jats:p>\u2022 posets of size &lt; <jats:italic>r<\/jats:italic> which add unbounded reals add Cohen reals.<\/jats:p><jats:p>We also show that add(<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200011348_inline1\" \/>) \u2264 min(r. r*). It follows that posets of size &lt; add(<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200011348_inline1\" \/>) which add reals add Cohen reals.<\/jats:p><jats:p>This improves results of Roslanowski and Shelah [RS] and of Zapletal [Z].<\/jats:p>","DOI":"10.2307\/2694924","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:03:53Z","timestamp":1146938633000},"page":"318-324","source":"Crossref","is-referenced-by-count":0,"title":["Cohen reals from small forcings"],"prefix":"10.1017","volume":"66","author":[{"given":"Janusz","family":"Pawlikowski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200011348_ref011","first-page":"280","volume":"62","author":"Zapletal","year":"1997","journal-title":"Small forcings and Cohen reals"},{"key":"S0022481200011348_ref010","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1986-033-8"},{"key":"S0022481200011348_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BF02760522"},{"key":"S0022481200011348_ref008","unstructured":"Roslanowski A. and Shelah S. , Simple forcing notions and forcing axioms, this Journal, to appear."},{"key":"S0022481200011348_ref006","doi-asserted-by":"publisher","DOI":"10.4064\/fm-102-3-173-181"},{"key":"S0022481200011348_ref005","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/5.1.108"},{"key":"S0022481200011348_ref003","doi-asserted-by":"publisher","DOI":"10.2307\/2044967"},{"key":"S0022481200011348_ref002","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":"S0022481200011348_ref001","first-page":"643","volume":"48","author":"Abraham","year":"1983","journal-title":"Forcing closed unbounded sets"},{"key":"S0022481200011348_ref004","first-page":"560","volume":"51","author":"Cicho\u0144","year":"1986","journal-title":"On ideals of subsets of the plane and on Cohen reals"},{"key":"S0022481200011348_ref007","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1981-0613787-2"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200011348","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,8]],"date-time":"2019-05-08T00:46:35Z","timestamp":1557276395000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200011348\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,3]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2001,3]]}},"alternative-id":["S0022481200011348"],"URL":"https:\/\/doi.org\/10.2307\/2694924","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,3]]}}}