[FOM] Existence of algebraic closures of fields

Aatu Koskensilta Aatu.Koskensilta at uta.fi
Sun Feb 28 15:42:47 EST 2010

Quoting Colin McLarty <colin.mclarty at case.edu>:

> Does the theorem that every field has an algebraic closure require the
> full strength of the axiom of choice?

No, the theorem is strictly weaker than choice. The compactness  
theorem for first-order logic, which Henkin proved equivalent to the  
prime ideal theorem, is all we need.

Aatu Koskensilta (aatu.koskensilta at uta.fi)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
  - Ludwig Wittgenstein, Tractatus Logico-Philosophicus

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