[FOM] Existence of algebraic closures of fields
wesley.calvert at murraystate.edu
Mon Mar 1 16:53:45 EST 2010
> Does the theorem that every field has an algebraic closure require the
> full strength of the axiom of choice? I mean relative to ZF, is that
> theorem equivalent to AC? The proofs I know of all refer to Zorn's
> lemma or existence of maximal ideas in ring, or the like. But did
> they need all of that?
Rabin's effective proof (Trans AMS 95 (1960) pp. 341--360) certainly
uses quite a lot less than AC.
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