{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,12,12]],"date-time":"2023-12-12T17:48:00Z","timestamp":1702403280124},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":11515,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1982,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that every formula of <jats:italic>L<jats:sub>\u03c9<jats:sub>1<\/jats:sub>P<\/jats:sub><\/jats:italic> is equivalent to one which is a propositional combination of formulas with only one quantifier. It follows that the complete theory of a probability model is determined by the distribution of a family of random variables induced by the model. We characterize the class of distribution which can arise in such a way. We use these results together with a form of de Finetti\u2019s theorem to prove an almost sure interpolation theorem for <jats:italic>L<jats:sub>\u03c9<jats:sub>1<\/jats:sub>P<\/jats:sub><\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2273591","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:00:58Z","timestamp":1146952858000},"page":"605-624","source":"Crossref","is-referenced-by-count":10,"title":["A normal form theorem for <i>L<sub>\u03c91p<\/sub><\/i>, with applications"],"prefix":"10.1017","volume":"47","author":[{"given":"Douglas N.","family":"Hoover","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120004398X_ref009","first-page":"183","volume":"34","author":"Krauss","year":"1969","journal-title":"Representations of symmetric probability models"},{"key":"S002248120004398X_ref011","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1953-0055421-1"},{"key":"S002248120004398X_ref003","volume-title":"Stochastic processes","author":"Doob","year":"1953"},{"key":"S002248120004398X_ref007","volume-title":"Logic Symposium '76","author":"Keisler","year":"1977"},{"key":"S002248120004398X_ref002","volume-title":"A course in probability theory","author":"Chung","year":"1974"},{"key":"S002248120004398X_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(81)90099-3"},{"key":"S002248120004398X_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF02759729"},{"key":"S002248120004398X_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(78)90022-0"},{"key":"S002248120004398X_ref006","unstructured":"Hoover D. N. , Model theory of probability logic, Ph.D. Thesis, University of Wisconsin-Madison, 1978."},{"key":"S002248120004398X_ref012","doi-asserted-by":"publisher","DOI":"10.2307\/1425935"},{"key":"S002248120004398X_ref008","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176995566"},{"key":"S002248120004398X_ref010","volume-title":"Probability theory","author":"Loeve","year":"1963"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120004398X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T20:47:35Z","timestamp":1558730855000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120004398X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,9]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1982,9]]}},"alternative-id":["S002248120004398X"],"URL":"https:\/\/doi.org\/10.2307\/2273591","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,9]]}}}