In this section we prove the completeness theorem for first-order logic. We shall prove it in its second form (Theorem 4.4.8). The result for countable theories was first proved by Gödel in 1930. The result in its complete generality was first observed by Malcev in 1936. The proof given below is due to Leo Henkin.
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(2008). Completeness Theorem and Model Theory. In: A Course on Mathematical Logic. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-0-387-76277-7_5
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