{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T18:33:50Z","timestamp":1761762830143},"reference-count":9,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":3969,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1996,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Two Fraenkel\u2010Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-sup-1.gif\" xlink:title=\"urn:x-wiley:09425616:media:MALQ19960420133:tex2gif-sup-1\" \/> and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second.<\/jats:p><jats:p>Mathematics Subject Classification: 03E25, 03E35, 04A25.<\/jats:p>","DOI":"10.1002\/malq.19960420133","type":"journal-article","created":{"date-parts":[[2007,5,30]],"date-time":"2007-05-30T11:25:16Z","timestamp":1180524316000},"page":"410-420","source":"Crossref","is-referenced-by-count":6,"title":["The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice"],"prefix":"10.1002","volume":"42","author":[{"given":"Paul","family":"Howard","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean E.","family":"Rubin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-127-1-57-66"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02007144"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-55-1-57-66"},{"key":"e_1_2_1_5_2","volume-title":"The Axiom of Choice","author":"Jech T.","year":"1973"},{"key":"e_1_2_1_6_2","volume-title":"General Topology","author":"Kelley J. L.","year":"1955"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","first-page":"137","DOI":"10.4064\/fm-33-1-137-168","article-title":"Axiom of choice for finite sets","volume":"33","author":"Mostowski A.","year":"1945","journal-title":"Fund. Math."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(77)90011-0"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(09)70445-8"},{"key":"e_1_2_1_10_2","first-page":"276","article-title":"Cardinals and the Boolean prime ideal theorem","volume":"13","author":"Tsukada N.","year":"1977","journal-title":"Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19960420133","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19960420133","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T22:11:43Z","timestamp":1698358303000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19960420133"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,1]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1996,1]]}},"alternative-id":["10.1002\/malq.19960420133"],"URL":"https:\/\/doi.org\/10.1002\/malq.19960420133","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,1]]}}}