Answer by Asaf Karagila for Is axiom of choice required for there to be an...
Yes. The axiom of choice is needed in order to show that every vector space which is not finitely generated contains an infinite linearly independent subset.The original consistency proof due to...
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In discussing this answer, I noted that while the statement:Any vector space has a basisis equivalent to the axiom of choice, I wondered if the statement that:Any vector space either has a finite basis...
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