{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T11:20:32Z","timestamp":1772450432676,"version":"3.50.1"},"reference-count":12,"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":192,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2013,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We develop a version of Namba forcing which is useful for constructing models with no good scale on \u2135<jats:italic><jats:sub>\u03c9<\/jats:sub><\/jats:italic>. A model is produced in which<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S002248120012660X_inline1\"\/>holds for all finite<jats:italic>n<\/jats:italic>\u2265 1, but there is no good scale on \u2135<jats:italic><jats:sub>\u03c9<\/jats:sub><\/jats:italic>; this strengthens a theorem of Cummings, Foreman, and Magidor [3] on the non-compactness of square.<\/jats:p>","DOI":"10.2178\/jsl.7803050","type":"journal-article","created":{"date-parts":[[2014,1,6]],"date-time":"2014-01-06T18:18:22Z","timestamp":1389032302000},"page":"785-802","source":"Crossref","is-referenced-by-count":2,"title":["Namba Forcing and No Good Scale"],"prefix":"10.1017","volume":"78","author":[{"given":"John","family":"Krueger","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120012660X_ref006","first-page":"175","volume":"62","author":"Foreman","year":"1997","journal-title":"A very weak square principle"},{"key":"S002248120012660X_ref007","doi-asserted-by":"publisher","DOI":"10.2307\/1971415"},{"key":"S002248120012660X_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2004.04.002"},{"key":"S002248120012660X_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2005.11.007"},{"key":"S002248120012660X_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12831-2"},{"key":"S002248120012660X_ref009","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1986-0831204-9"},{"key":"S002248120012660X_ref003","first-page":"637","volume":"68","author":"Cummings","year":"2003","journal-title":"The non-compactness of square"},{"key":"S002248120012660X_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF02761160"},{"key":"S002248120012660X_ref010","first-page":"1","article-title":"Independence proof of (\u03c9, \u03c9\u03b1 )-distributivity law in complete Boolean algebras","volume":"19","author":"Namba","year":"1970","journal-title":"Com-mentarii Mathematici Universitatis Sancti Pauli"},{"key":"S002248120012660X_ref011","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198537854.001.0001","volume-title":"Cardinal arithmetic","volume":"29","author":"Shelah","year":"1994"},{"key":"S002248120012660X_ref001","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1125409326"},{"key":"S002248120012660X_ref002","doi-asserted-by":"publisher","DOI":"10.1142\/S021906130100003X"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120012660X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,22]],"date-time":"2024-05-22T16:06:00Z","timestamp":1716393960000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120012660X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,9]]}},"alternative-id":["S002248120012660X"],"URL":"https:\/\/doi.org\/10.2178\/jsl.7803050","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,9]]}}}