{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,30]],"date-time":"2023-10-30T07:36:59Z","timestamp":1698651419741},"reference-count":9,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2007,5,18]],"date-time":"2007-05-18T00:00:00Z","timestamp":1179446400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2007,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Two theorems are proved: First that the statement<\/jats:p><jats:p>\u201cthere exists a field <jats:italic>F<\/jats:italic> such that for every vector space over <jats:italic>F<\/jats:italic>, every generating set contains a basis\u201d<\/jats:p><jats:p>implies the axiom of choice. This generalizes theorems of Halpern, Blass, and Keremedis. Secondly, we prove that the assertion that every vector space over \u2124<jats:sub>2<\/jats:sub> has a basis implies that every well\u2010ordered collection of two\u2010element sets has a choice function. (\u00a9 2007 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200610043","type":"journal-article","created":{"date-parts":[[2007,5,18]],"date-time":"2007-05-18T22:44:29Z","timestamp":1179528269000},"page":"247-254","source":"Crossref","is-referenced-by-count":1,"title":["Bases, spanning sets, and the axiom of choice"],"prefix":"10.1002","volume":"53","author":[{"given":"Paul","family":"Howard","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,5,18]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","first-page":"145","DOI":"10.4064\/fm-74-2-145-146","article-title":"An algebraic equivalent of the multiple choice axiom","volume":"74","author":"Armbrust M. K.","year":"1972","journal-title":"Fund. Math."},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"A.Blass Existence of a basis implies the axiom of choice. In: Axiomatic Set Theory (J. Baumgartner D. A. Martin and S. Shelah eds.). Contemporary Mathematics 31 pp. 31\u201333 (AMS 1984).","DOI":"10.1090\/conm\/031\/763890"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","first-page":"95","DOI":"10.4064\/fm-54-1-95-107","article-title":"Some theorems on vector spaces and the axiom of choice","volume":"54","author":"Bleicher M. N.","year":"1964","journal-title":"Fund. Math."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/2035388"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19730191103"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","unstructured":"P.Howard andJ. E.Rubin Consequences of the Axiom of Choice. AMS Math. Surveys and Monographs 59 (1998). Available athttp:\/\/consequences.emich.edu\/","DOI":"10.1090\/surv\/059"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-96-03305-9"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/1521-3870(200105)47:2<205::AID-MALQ205>3.0.CO;2-I"},{"key":"e_1_2_1_10_2","unstructured":"H.Rubin andJ.Rubin Equivalents of the Axiom of Choice II (North\u2010Holland 1985)."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200610043","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200610043","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T15:05:03Z","timestamp":1697641503000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200610043"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,5,18]]},"references-count":9,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2007,6]]}},"alternative-id":["10.1002\/malq.200610043"],"URL":"https:\/\/doi.org\/10.1002\/malq.200610043","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,5,18]]}}}