{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T11:56:19Z","timestamp":1759146979821},"reference-count":9,"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":14802,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1973,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The Fraenkel-Mostowski method has been widely used to prove independence results among weak versions of the axiom of choice. In this paper it is shown that certain statements cannot be proved by this method. More specifically it is shown that in all Fraenkel-Mostowski models the following hold:<\/jats:p><jats:p>1. The axiom of choice for sets of finite sets implies the axiom of choice for sets of well-orderable sets.<\/jats:p><jats:p>2. The Boolean prime ideal theorem implies a weakened form of Sikorski's theorem.<\/jats:p>","DOI":"10.2307\/2273037","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:24:44Z","timestamp":1146950684000},"page":"416-422","source":"Crossref","is-referenced-by-count":11,"title":["Limitations on the Fraenkel-Mostowski method of independence proofs"],"prefix":"10.1017","volume":"38","author":[{"given":"Paul E.","family":"Howard","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200054773_ref003","doi-asserted-by":"crossref","first-page":"57","DOI":"10.4064\/fm-55-1-57-66","article-title":"The independence of the axiom of choice from the Boolean prime ideal theorum","volume":"55","author":"Halpern","year":"1963","journal-title":"Fundamenta Mathematicae"},{"key":"S0022481200054773_ref005","volume-title":"International Symposium on the Theory of Models","author":"Levy","year":"1965"},{"key":"S0022481200054773_ref008","doi-asserted-by":"crossref","first-page":"201","DOI":"10.4064\/fm-32-1-201-252","article-title":"\u00dcber die Unabhangigkeit des Wohlordnungssatz vom Ordnungsprinzip","volume":"32","author":"Mostowski","year":"1939","journal-title":"Fundamenta Mathematicae"},{"key":"S0022481200054773_ref007","doi-asserted-by":"crossref","first-page":"137","DOI":"10.4064\/fm-33-1-137-168","article-title":"The axiom of choice for finite sets","volume":"33","author":"Mostowski","year":"1945","journal-title":"Fundamenta Mathematicae"},{"key":"S0022481200054773_ref002","first-page":"454","article-title":"Axiom of choice for finite sets\u2014a solution to a problem of Mostowski","volume":"17","author":"Gauntt","year":"1970","journal-title":"Notices of the American Mathematical Society"},{"key":"S0022481200054773_ref001","first-page":"351","article-title":"Some restricted versions of the axiom of choice","volume":"15","author":"Gauntt","year":"1968","journal-title":"Notices of the American Mathematical Society"},{"key":"S0022481200054773_ref009","volume-title":"Boolean algebras","author":"Sikorski","year":"1964"},{"key":"S0022481200054773_ref006","doi-asserted-by":"crossref","first-page":"127","DOI":"10.4064\/fm-35-1-127-130","article-title":"On the principle of dependent choices","volume":"35","author":"Mostowski","year":"1948","journal-title":"Fundamenta Mathematicae"},{"key":"S0022481200054773_ref004","doi-asserted-by":"crossref","first-page":"31","DOI":"10.4064\/fm-54-1-31-43","article-title":"The independence of the ordering principle from a restricted axiom of choice","volume":"54","author":"Lauchli","year":"1963","journal-title":"Fundamenta Mathematicae"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200054773","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T19:38:10Z","timestamp":1559245090000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200054773\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1973,9]]},"references-count":9,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1973,9]]}},"alternative-id":["S0022481200054773"],"URL":"https:\/\/doi.org\/10.2307\/2273037","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1973,9]]}}}