MATHEUS DE ARAÚJO FERREIRA

This research aims to study some aspects of the relationship between the Axiom of Choice and the idea of semantic completeness of logical calculi, and is structured in three stages. The first one turns to a brief historical investigation of the Axiom and its contribution to Logic in the 20th Century, lending special attention to the proof of the Gödel-Malcev-Henkin Completeness Theorem for First Order Logic. The second one seeks to extend the scope of the subject by resorting to certain notions and tools from Abstract Logic, focusing on the analysis of the two main versions of Lindenbaum's Theorem – an essential lemma for completeness proofs of logical calculi in general. The third and final stage consists in presenting and examining in detail the proofs of equivalence between Lindenbaum's Theorem and the Axiom of Choice provided by Dzik (1981) and Miller (2007), reflecting on the conceptual scope of that result.