{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T08:13:06Z","timestamp":1772179986775,"version":"3.50.1"},"reference-count":8,"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":13068,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1978,6]]},"abstract":"<jats:p>Let <jats:italic>L<\/jats:italic> be a countable language including the unary relation symbol <jats:italic>U<\/jats:italic>. Let <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200049677_inline1\"\/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200049677_inline2\"\/> be L-structures such that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200049677_inline2\"\/> is a proper elementary <jats:italic>U<\/jats:italic>-extension of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200049677_inline1\"\/>; i.e., <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200049677_inline3\"\/>, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200049677_inline4\"\/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200049677_inline5\"\/>. Under what conditions will <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200049677_inline1\"\/> have a proper elementary <jats:italic>U<\/jats:italic>-extension? In [2], it was shown that this is not always the case, even if <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200049677_inline1\"\/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200049677_inline2\"\/> are countable. However, the examples given are completely artificial, and it still seems that in most cases <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200049677_inline2\"\/><jats:italic>will<\/jats:italic> have a proper elementary <jats:italic>U<\/jats:italic>-extension.<\/jats:p><jats:p>Lascar asked whether <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200049677_inline2\"\/> will necessarily have a proper elementary <jats:italic>U<\/jats:italic>-extension whenever it contains an infinite set of indiscernibles over <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200049677_inline1\"\/>. This paper gives a counterexample for Lascar's question. The example is produced by modifying one of the examples in [2], using an idea of Marcus [5].<\/jats:p><jats:p>Models containing an infinite set of indiscernibles can often be \u201cstretched\u201d to produce larger models that share some desired nonelementary property with the original [1], [6]. However, the mere presence of indiscernibles in a model does not guarantee that it can be used in this way.<\/jats:p><jats:p>If the model is not completely determined by the indiscernibles, the nonelementary property may not carry over to larger models. An example of this is given in [3]. The example for Lascar's question is further evidence that models with indiscernibles need not be \u201celastic\u201d.<\/jats:p>","DOI":"10.2307\/2272831","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:47:35Z","timestamp":1146952055000},"page":"331-334","source":"Crossref","is-referenced-by-count":2,"title":["An inelastic model with indiscernibles"],"prefix":"10.1017","volume":"43","author":[{"given":"Julia F.","family":"Knight","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200049677_ref007","first-page":"107","volume":"37","author":"Shelah","year":"1972","journal-title":"Uniqueness and characterization of prime models over sets for totally transcendental first order theories"},{"key":"S0022481200049677_ref004","unstructured":"Knight J. , Prime and atomic models, preprint."},{"key":"S0022481200049677_ref001","doi-asserted-by":"publisher","DOI":"10.4064\/fm-43-1-50-68"},{"key":"S0022481200049677_ref006","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1965-0175782-0"},{"key":"S0022481200049677_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BF02762619"},{"key":"S0022481200049677_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF02757882"},{"key":"S0022481200049677_ref002","first-page":"561","volume":"38","author":"Knight","year":"1973","journal-title":"Generic expansions of structures"},{"key":"S0022481200049677_ref003","first-page":"25","volume":"41","author":"Knight","year":"1976","journal-title":"Omitting types in set theory and arithmetic"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200049677","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,27]],"date-time":"2019-05-27T19:57:38Z","timestamp":1558987058000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200049677\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1978,6]]},"references-count":8,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1978,6]]}},"alternative-id":["S0022481200049677"],"URL":"https:\/\/doi.org\/10.2307\/2272831","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1978,6]]}}}