{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T13:31:39Z","timestamp":1781789499093,"version":"3.54.5"},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":15717,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1971,3]]},"abstract":"<jats:p>The purpose of this paper is twofold. In \u00a71 and \u00a72 which are largely expository we develop the known theory of \u2135<jats:sub>1<\/jats:sub>-categoricity in terms of strongly minimal sets. In \u00a73 we settle affirmatively Vaught's conjecture that a complete \u2135<jats:sub>1<\/jats:sub>-categorical theory has either just one or just \u2135<jats:sub>0<\/jats:sub> countable models, and in \u00a74 we present an example which serves to illustrate the ideas of \u00a73.<\/jats:p><jats:p>As far as we know the only work published on strongly minimal sets is that of Marsh [3]. The present exposition goes beyond [3] in showing that any \u2135-categorical theory has a principal extension in which some formula is strongly minimal.<\/jats:p>","DOI":"10.2307\/2271517","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T17:05:56Z","timestamp":1146935156000},"page":"79-96","source":"Crossref","is-referenced-by-count":143,"title":["On strongly minimal sets"],"prefix":"10.1017","volume":"36","author":[{"given":"J. T.","family":"Baldwin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A. H.","family":"Lachlan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120008395X_ref001","first-page":"23","article-title":"Ultraproducts which are not saturated","volume":"32","author":"Keisler","year":"1967","journal-title":"this Journal"},{"key":"S002248120008395X_ref007","unstructured":"Park D. M. R. , Set theoretic constructions in model theory, Doctoral Dissertation, Massachusetts Institute of Technology, 1964."},{"key":"S002248120008395X_ref009","first-page":"303","volume-title":"Proceedings of the Symposium on Foundations of Mathematics: Infinitistic methods","author":"Vaught","year":"1961"},{"key":"S002248120008395X_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BF02771623"},{"key":"S002248120008395X_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BF02771640"},{"key":"S002248120008395X_ref003","unstructured":"Marsh W. E. , On \u03c91-categorical but not \u03c9-categorical theories, Doctoral Dissertation, Dartmouth College, 1966."},{"key":"S002248120008395X_ref006","doi-asserted-by":"publisher","DOI":"10.7146\/math.scand.a-10648"},{"key":"S002248120008395X_ref004","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1965-0175782-0"},{"key":"S002248120008395X_ref008","volume-title":"Mathematical logic","author":"Shoenfield","year":"1967"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120008395X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T16:20:19Z","timestamp":1559319619000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120008395X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1971,3]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1971,3]]}},"alternative-id":["S002248120008395X"],"URL":"https:\/\/doi.org\/10.2307\/2271517","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1971,3]]}}}