{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,8,5]],"date-time":"2022-08-05T15:10:48Z","timestamp":1659712248177},"reference-count":4,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":3571,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2004,6]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>For a stationary set <jats:italic>S<\/jats:italic> \u2286 \u03c9<jats:sub>1<\/jats:sub>, and a ladder system <jats:italic>C<\/jats:italic> over <jats:italic>S<\/jats:italic>, a new type of gaps called <jats:italic>C<\/jats:italic>-Hausdorff is introduced and investigated. We describe a forcing model of ZFC in which, for some stationary set <jats:italic>S<\/jats:italic>, for every ladder <jats:italic>C<\/jats:italic> over <jats:italic>S<\/jats:italic>, every gap contains a subgap that is <jats:italic>C<\/jats:italic>-Hausdorff. But for every ladder <jats:italic>E<\/jats:italic> over \u03c9<jats:sub>1<\/jats:sub> \u2216 <jats:italic>S<\/jats:italic> there exists a gap with no subgap that is <jats:italic>E<\/jats:italic>-Hausdorff.<\/jats:p><jats:p>A new type of chain condition, called polarized chain condition, is introduced. We prove that the iteration with finite support of polarized c.c.c. posets is again a polarized c.c.c. poset.<\/jats:p>","DOI":"10.2178\/jsl\/1082418541","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T21:37:28Z","timestamp":1109799448000},"page":"518-532","source":"Crossref","is-referenced-by-count":2,"title":["Ladder gaps over stationary sets"],"prefix":"10.1017","volume":"69","author":[{"given":"Uri","family":"Abraham","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saharon","family":"Shelah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120000788X_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)00020-4"},{"key":"S002248120000788X_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0016-660X(72)90001-3"},{"key":"S002248120000788X_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(70)90009-4"},{"key":"S002248120000788X_ref003","first-page":"439","volume-title":"Set Theory of the Reals","volume":"6","author":"Scheepers","year":"1991"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120000788X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T21:02:46Z","timestamp":1557176566000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120000788X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,6]]},"references-count":4,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2004,6]]}},"alternative-id":["S002248120000788X"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1082418541","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,6]]}}}