{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T15:51:08Z","timestamp":1724428268171},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":3388,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2004,12]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>The authors show, by means of a finitary version <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200007507_inline1\" \/> of the combinatorial principle <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200007507_inline2\" \/> of [7]. the consistency of the failure, relative to the consistency of supercompact cardinals, of the following: for all regular filters <jats:italic>D<\/jats:italic> on a cardinal \u03bb. if <jats:italic>M<jats:sub>i<\/jats:sub><\/jats:italic> and <jats:italic>N<jats:sub>i<\/jats:sub><\/jats:italic> are elementarily equivalent models of a language of size \u2264 \u03bb, then the second player has a winning strategy in the Ehrenfeucht-Fra\u00efss\u00e9 game of length \u03bb<jats:sup>+<\/jats:sup> on \u03a0<jats:sub><jats:italic>i<\/jats:italic><\/jats:sub><jats:italic>M<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>\/<jats:italic>D<\/jats:italic> and \u03a0<jats:italic><jats:sub>i<\/jats:sub><\/jats:italic><jats:italic>N<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>\/<jats:italic>D<\/jats:italic>. If in addition 2<jats:sup>\u03bb<\/jats:sup> = \u03bb<jats:sup>+<\/jats:sup> and <jats:italic>i<\/jats:italic> &lt; \u03bb implies |<jats:italic>M<jats:sub>i<\/jats:sub><\/jats:italic>| + |<jats:italic>N<jats:sub>i<\/jats:sub><\/jats:italic>| \u2264 \u03bb<jats:sup>+<\/jats:sup> this means that the ultrapowers are isomorphic. This settles negatively conjecture 18 in [2].<\/jats:p>","DOI":"10.2178\/jsl\/1102022222","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T21:52:35Z","timestamp":1109800355000},"page":"1261-1266","source":"Crossref","is-referenced-by-count":3,"title":["More on regular reduced products"],"prefix":"10.1017","volume":"69","author":[{"given":"Juliette Cara","family":"Kennedy","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":"S0022481200007507_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF02771574"},{"key":"S0022481200007507_ref005","doi-asserted-by":"publisher","DOI":"10.4064\/fm176-1-2"},{"key":"S0022481200007507_ref004","first-page":"1169\u20131177","volume":"67","author":"Kennedy","year":"2002","journal-title":"On regular reduced products"},{"key":"S0022481200007507_ref002","volume-title":"Model theory","author":"Chang","year":"1990"},{"key":"S0022481200007507_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF02761504"},{"key":"S0022481200007507_ref003","first-page":"178\u2013186","volume-title":"Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings Series A","volume":"67","author":"Keisler","year":"1964"},{"key":"S0022481200007507_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02764857"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200007507","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T19:38:54Z","timestamp":1557171534000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200007507\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,12]]},"references-count":7,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2004,12]]}},"alternative-id":["S0022481200007507"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1102022222","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,12]]}}}