{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T10:32:06Z","timestamp":1775644326112,"version":"3.50.1"},"reference-count":10,"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":9689,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1987,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A model of ZFC is constructed in which the distributivity cardinal <jats:bold>h<\/jats:bold> is <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481200029662_inline1.png\"\/>, and in which there are no <jats:italic>\u03c9<\/jats:italic><jats:sub>2<\/jats:sub>-towers in [<jats:italic>\u03c9<\/jats:italic>]<jats:italic>\u03c9<\/jats:italic>. As an immediate corollary, it follows that any base-matrix tree in this model has no cofinal branches. The model is constructed via a form of iterated Mathias forcing, in which a mixture of finite and countable supports is used.<\/jats:p>","DOI":"10.2307\/2274354","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:22:39Z","timestamp":1146954159000},"page":"651-664","source":"Crossref","is-referenced-by-count":17,"title":["A model in which the base-matrix tree cannot have cofinal branches"],"prefix":"10.1017","volume":"52","author":[{"given":"Peter Lars","family":"Dordal","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200029662_bib005","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-444-86580-9.50006-9"},{"key":"S0022481200029662_bib008","volume-title":"Set theory","author":"Jech","year":"1978"},{"key":"S0022481200029662_bib003","first-page":"94","volume":"50","author":"Baumgartner","year":"1985","journal-title":"Adjoining dominating functions"},{"key":"S0022481200029662_bib006","unstructured":"Dow, A. , Tree \u03a0-bases for \u03b2N \u2013 N in various models (to appear)."},{"key":"S0022481200029662_bib002","first-page":"1","volume-title":"Surveys in set theory","author":"Baumgartner","year":"1983"},{"key":"S0022481200029662_bib001","doi-asserted-by":"publisher","DOI":"10.4064\/fm-110-1-11-24"},{"key":"S0022481200029662_bib004","unstructured":"Dordal, P. , Independence results concerning some combinatorial properties of the continuum, Ph.D. Dissertation, Harvard University, Cambridge, Massachusetts, 1982."},{"key":"S0022481200029662_bib009","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/BF02392416","article-title":"On the consistency of Borel's conjecture","volume":"137","author":"Laver","year":"1976","journal-title":"Acta Mathematica"},{"key":"S0022481200029662_bib007","doi-asserted-by":"publisher","DOI":"10.4064\/fm-26-1-241-255"},{"key":"S0022481200029662_bib010","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(72)90017-4"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200029662","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T10:39:12Z","timestamp":1679481552000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200029662\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1987,9]]},"references-count":10,"aliases":["10.1017\/s0022481200029662"],"journal-issue":{"issue":"3","published-print":{"date-parts":[[1987,9]]}},"alternative-id":["S0022481200029662"],"URL":"https:\/\/doi.org\/10.2307\/2274354","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1987,9]]}}}