{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T18:57:36Z","timestamp":1648666656439},"reference-count":18,"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":7041,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1994,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper we establish the following theorems.<\/jats:p><jats:p>Theorem A. <jats:italic>Let T be a complete first-order theory which is uncountable, Then<\/jats:italic>:<\/jats:p><jats:p>(i) <jats:italic>I<\/jats:italic>(\u2223<jats:italic>T<\/jats:italic>\u2223, <jats:italic>T<\/jats:italic>) \u2265 \u2135<jats:sub>0<\/jats:sub><\/jats:p><jats:p>(ii) <jats:italic>If T is not unidimensional, then for any \u03bb<\/jats:italic> \u2265 \u2223<jats:italic>T<\/jats:italic>\u2223, <jats:italic>I(\u03bb, T<\/jats:italic>) \u2265 \u2135<jats:sub>0<\/jats:sub>.<\/jats:p><jats:p>Theorem B. <jats:italic>Let T be superstable, not totally transcendental and nonmultidimensional. Let \u03b8(<jats:italic>x<\/jats:italic>) be a formula of least R<jats:sup>\u221e<\/jats:sup> rank which does not have Morley rank, and let p be any stationary completion of \u03b8 which also fails to have Morley rank. Then p is regular and locally modular<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2275706","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:53:29Z","timestamp":1146956009000},"page":"1285-1300","source":"Crossref","is-referenced-by-count":2,"title":["On the number of models of uncountable theories"],"prefix":"10.1017","volume":"59","author":[{"given":"Ambar","family":"Chowdhury","sequence":"first","affiliation":[]},{"given":"Anand","family":"Pillay","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200019289_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF01277487"},{"key":"S0022481200019289_ref004","volume-title":"Contributions to stable model theory","author":"Hrushovski","year":"1986"},{"key":"S0022481200019289_ref010","first-page":"512","volume":"53","author":"Laskowski","year":"1988","journal-title":"Uncountable theories that are categorical in a higher power"},{"key":"S0022481200019289_ref002","first-page":"1044","volume":"50","author":"Buechler","year":"1985","journal-title":"The geometry of weakly minimal types"},{"key":"S0022481200019289_ref017","first-page":"73","volume":"35","author":"Shelah","year":"1970","journal-title":"On theories T categorical in \u2223T\u2223"},{"key":"S0022481200019289_ref013","unstructured":"Pillay A. , Geometric stability theory , forthcoming."},{"key":"S0022481200019289_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-07330-8"},{"key":"S0022481200019289_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0082236"},{"key":"S0022481200019289_ref008","first-page":"45","volume-title":"Logic, Methodology and Philosophy of Science IV","author":"Lachlan","year":"1973"},{"key":"S0022481200019289_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BF02760649"},{"key":"S0022481200019289_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(90)90078-G"},{"key":"S0022481200019289_ref014","first-page":"151","volume":"59","author":"Pillay","year":"1994","journal-title":"Some remarks on nonmultidimensional superstable theories"},{"key":"S0022481200019289_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/BF01634980"},{"key":"S0022481200019289_ref016","volume-title":"Groupes stables","author":"Poizat","year":"1987"},{"key":"S0022481200019289_ref018","volume-title":"Classification theory","author":"Shelah","year":"1990"},{"key":"S0022481200019289_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(89)90059-6"},{"key":"S0022481200019289_ref009","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1975.61.465"},{"key":"S0022481200019289_ref003","first-page":"41","volume":"59","author":"Chowdhury","year":"1994","journal-title":"On the number of nonisomorphic models of size \u2223T\u2223"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200019289","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T00:41:11Z","timestamp":1557880871000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200019289\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,12]]},"references-count":18,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1994,12]]}},"alternative-id":["S0022481200019289"],"URL":"https:\/\/doi.org\/10.2307\/2275706","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,12]]}}}