{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,30]],"date-time":"2023-10-30T07:40:43Z","timestamp":1698651643562},"reference-count":8,"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":3238,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1998,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that the both assertions \u201cin every vector space <jats:italic>B<\/jats:italic> over a finite element field every subspace <jats:italic>V<\/jats:italic> \u2286 <jats:italic>B<\/jats:italic> has a complementary subspace <jats:italic>S<\/jats:italic>\u201d and \u201cfor every family \ud835\udc9c of disjoint odd sized sets there exists a subfamily \u2131={F<jats:sub>j<\/jats:sub>:j \u03f5\u03c9} with a choice function\u201d together imply the axiom of choice AC. We also show that AC is equivalent to the statement \u201cin every vector space over \u211a every generating set includes a basis\u201d.<\/jats:p>","DOI":"10.1002\/malq.19980440106","type":"journal-article","created":{"date-parts":[[2007,5,31]],"date-time":"2007-05-31T03:02:07Z","timestamp":1180580527000},"page":"92-98","source":"Crossref","is-referenced-by-count":3,"title":["Extending Independent Sets to Bases and the Axiom of Choice"],"prefix":"10.1002","volume":"44","author":[{"given":"Kyriakos","family":"Keremedis","sequence":"first","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":"10.1090\/conm\/031\/763890"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1090\/S0002-9947-1979-0542870-6","article-title":"Injectivity, projectivity, and the axiom of choice","volume":"255","author":"Blass A.","year":"1979","journal-title":"Trans. Amer. Math. Soc."},{"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.","year":"1964","journal-title":"Fund. Math."},{"key":"e_1_2_1_5_2","unstructured":"Howard P. A. L.Rubin andJ. E.Rubin Kinna\u2010Wagner selection principles axioms of choice and multiple choice. Preprint1995."},{"key":"e_1_2_1_6_2","unstructured":"Howard P. andJ.Rubin Weak forms of AC. In preparation."},{"key":"e_1_2_1_7_2","volume-title":"The Axiom of Choice","author":"Jech T.","year":"1973"},{"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","volume-title":"Equivalents of the Axiom of Choice II","author":"Rubin H.","year":"1985"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19980440106","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19980440106","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,28]],"date-time":"2023-10-28T12:55:06Z","timestamp":1698497706000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19980440106"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["10.1002\/malq.19980440106"],"URL":"https:\/\/doi.org\/10.1002\/malq.19980440106","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}