{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T05:03:12Z","timestamp":1648875792960},"reference-count":15,"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":8685,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1990,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>T<\/jats:italic> be a complete countable first order theory and <jats:italic>\u03bb<\/jats:italic> an uncountable cardinal. T<jats:sc>heorem<\/jats:sc> 1. <jats:italic>If T is not superstable, T has 2<jats:sup>\u03bb<\/jats:sup> resplendent models of power \u03bb<\/jats:italic>. T<jats:sc>heorem<\/jats:sc> 2. <jats:italic>If T is strictly superstable, then T has at least<\/jats:italic> min(2<jats:sup><jats:italic>\u03bb<\/jats:italic><\/jats:sup>, \u2136<jats:sub>2<\/jats:sub>) <jats:italic>resplendent models of power \u03bb<\/jats:italic>. T<jats:sc>heorem<\/jats:sc> 3. <jats:italic>If T is not superstable or is small and strictly superstable, then every resplendent homogeneous model of T is saturated<\/jats:italic>. T<jats:sc>heorem<\/jats:sc> 4 (with K<jats:sc>night<\/jats:sc>). <jats:italic>For each<\/jats:italic> \u03bc \u2208 \u03c9 \u222a {\u03c9, 2<jats:sup>\u03c9<\/jats:sup>} <jats:italic>there is a recursive theory in a finite language which has \u03bc resplendent models of power \u03ba for every infinite \u03ba<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2274652","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:35:29Z","timestamp":1146954929000},"page":"626-636","source":"Crossref","is-referenced-by-count":0,"title":["The spectrum of resplendency"],"prefix":"10.1017","volume":"55","author":[{"given":"John T.","family":"Baldwin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200026025_ref001","first-page":"875","volume":"54","author":"Baldwin","year":"1989","journal-title":"Diverse classes"},{"key":"S0022481200026025_ref006","first-page":"222","volume":"51","author":"Knight","year":"1986","journal-title":"Saturation of homogeneous resplendent models"},{"key":"S0022481200026025_ref011","volume-title":"One theorem on the number of uncountable models","author":"Saffe","year":"1983"},{"key":"S0022481200026025_ref009","volume-title":"Cours de th\u00e9orie des mod\u00e8les","author":"Poizat","year":"1985"},{"key":"S0022481200026025_ref012","volume-title":"Classification theory and the number of non-isomorphic models","author":"Shelah","year":"1978"},{"key":"S0022481200026025_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02765017"},{"key":"S0022481200026025_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0082234"},{"key":"S0022481200026025_ref014","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(87)90020-0"},{"key":"S0022481200026025_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-07330-8"},{"key":"S0022481200026025_ref003","first-page":"531","volume":"41","author":"Barwise","year":"1976","journal-title":"An introduction to recursively saturated and resplendent models"},{"key":"S0022481200026025_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF02760644"},{"key":"S0022481200026025_ref008","first-page":"587","volume":"47","author":"Knight","year":"1982","journal-title":"Expansions of models and Turing degrees"},{"key":"S0022481200026025_ref015","first-page":"265","volume-title":"Classification theory: Chicago, 1985","volume":"1292","author":"Shelah","year":"1987"},{"key":"S0022481200026025_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)70461-0"},{"key":"S0022481200026025_ref013","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(70)90007-0"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200026025","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T21:14:20Z","timestamp":1558214060000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200026025\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,6]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1990,6]]}},"alternative-id":["S0022481200026025"],"URL":"https:\/\/doi.org\/10.2307\/2274652","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,6]]}}}