{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T11:49:16Z","timestamp":1759146556929},"reference-count":7,"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":10603,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1985,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>If dominating functions in <jats:sup><jats:italic>\u03c9<\/jats:italic><\/jats:sup><jats:italic>\u03c9<\/jats:italic> are adjoined repeatedly over a model of GCH via a finite-support c.c.c. iteration, then in the resulting generic extension there are no long towers, every well-ordered unbounded family of increasing functions is a scale, and the splitting number <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200033107_inline1\" \/> (and hence the distributivity number <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200033107_inline2\" \/>) remains at <jats:italic>\u03c9<\/jats:italic><jats:sub>1<\/jats:sub>.<\/jats:p>","DOI":"10.2307\/2273792","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:12:14Z","timestamp":1146953534000},"page":"94-101","source":"Crossref","is-referenced-by-count":36,"title":["Adjoining dominating functions"],"prefix":"10.1017","volume":"50","author":[{"given":"James E.","family":"Baumgartner","sequence":"first","affiliation":[]},{"given":"Peter","family":"Dordal","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200033107_ref002","unstructured":"Dordal P. , Independence results concerning some combinatorial properties of the continuum, Ph.D. Dissertation, Harvard University, Cambridge, Massachusetts, 1982."},{"key":"S0022481200033107_ref007","doi-asserted-by":"publisher","DOI":"10.4064\/fm-35-1-29-46"},{"key":"S0022481200033107_ref001","first-page":"1","volume-title":"Surveys in set theory","author":"Baumgartner","year":"1983"},{"key":"S0022481200033107_ref003","volume-title":"The handbook of set-theoretic topology","author":"van Douwen","year":"1984"},{"key":"S0022481200033107_ref006","doi-asserted-by":"publisher","DOI":"10.4064\/fm-102-3-173-181"},{"key":"S0022481200033107_ref004","volume-title":"Set theory","author":"Jech","year":"1978"},{"key":"S0022481200033107_ref005","volume-title":"Set theory","author":"Kunen","year":"1980"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200033107","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,22]],"date-time":"2019-05-22T23:23:11Z","timestamp":1558567391000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200033107\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,3]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1985,3]]}},"alternative-id":["S0022481200033107"],"URL":"https:\/\/doi.org\/10.2307\/2273792","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1985,3]]}}}