A note on the Artin-Schreier Theorem
By F. G. Dorais
unpublished note
In this note, I give a direct elementary proof of the equivalence of the Artin–Schreier Theorem with the Completeness Theorem for propositional logic. This gives another proof a result of Berr, Delon and Schmid that the Artin–Schreier Theorem is equivalent to the Ultrafilter Theorem over ZF.