Deductive Systems and the Lemma of Lindenbaum

Tarski axiomatizes inferability respectively Provability in a formal language using deductive systems. In this abstract context, the Lindenbaum’s theorem (every consistent set can be extended to a maximally consistent set) in a very general way. It turns out, that this theorem is equivalent to the axiom of choice. Just show the connections between Tarski, Lindenbaum and the axiom of choice. 10 pages would be nice. If you know more sources, you can go up to 20 pages.

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