[FOM] Existence of algebraic closures of fields

Colin McLarty colin.mclarty at case.edu
Sun Feb 28 09:51:31 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?

thanks, Colin

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