{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T02:42:11Z","timestamp":1649040131948},"reference-count":5,"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":1562,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2009,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In partial answer to a question posed by Arnie Miller [4] and X. Caicedo [2] we obtain sufficient conditions for an \u2112<jats:sub><jats:italic>\u03c9<\/jats:italic>1,<jats:italic>\u03c9<\/jats:italic><\/jats:sub> theory to have an independent axiomatization. As a consequence we obtain two corollaries: The first, assuming Vaught's Conjecture, every \u2112<jats:sub><jats:italic>\u03c9<\/jats:italic>1,<jats:italic>\u03c9<\/jats:italic><\/jats:sub> theory in a countable language has an independent axiomatization. The second, this time outright in ZFC, every intersection of a family of Borel sets can be formed as the intersection of a family of <jats:italic>independent<\/jats:italic> Borel sets.<\/jats:p>","DOI":"10.2178\/jsl\/1254748691","type":"journal-article","created":{"date-parts":[[2009,10,5]],"date-time":"2009-10-05T13:05:40Z","timestamp":1254747940000},"page":"1273-1286","source":"Crossref","is-referenced-by-count":0,"title":["Independently axiomatizable \u2112<sub>\u03c91,\u03c9<\/sub> theories"],"prefix":"10.1017","volume":"74","author":[{"given":"Greg","family":"Hjorth","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ioannis A.","family":"Souldatos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200003157_ref005","first-page":"2385","article-title":"Tout ensemble de formules de la logique classique est equivalent \u00e0 un ensemble independant","volume":"260","author":"Reznikoff","year":"1965","journal-title":"Comptes Rendus Math\u00e9matique. Acad\u00e9mie des Sciences. Paris"},{"key":"S0022481200003157_ref004","unstructured":"Miller Arnold W. , http:\/\/www.math.wise.edu\/~miller\/res\/problem.pdf, This webpage contains a list of interesting problems in Set Theory and Model Theory."},{"key":"S0022481200003157_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4190-4"},{"key":"S0022481200003157_ref001","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511735264"},{"key":"S0022481200003157_ref002","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1981-034-x"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200003157","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,29]],"date-time":"2019-04-29T18:35:22Z","timestamp":1556562922000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200003157\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12]]},"references-count":5,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,12]]}},"alternative-id":["S0022481200003157"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1254748691","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,12]]}}}