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See D.Hilbert & W.Ackermann, Principles of Mathematical Logic: the 1950 American translation of the 1938 second edition of Grundzüge der theoretischen Logik. The 1928 first edition is considered the first elementary text exposing the formalism now known as first-order logic. See §9 The Consistency and Independence of the System of Axioms, page 87-on. The ...


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Gödel first proved the soundness theorem in his completeness theorem in 1930 based on proof theory ("Die Vollständigkeit der Axiome des logischen Funktionenkalküls"). The model-theoretic proof of the soundness theorem, i.e. a set of sentences is consistent if and only if they have a model, was first given by Henkin in 1949. However, the ...


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