Henkin on Completeness

The Completeness of Formal Systems is the title of the thesis that Henkin presented at Princeton in 1947 under the supervision of Alonzo Church. A few years after the defense of his thesis, Henkin published two papers in the Journal of Symbolic Logic: the first, on completeness for first-order logic (Henkin in J. Symb. Log. 14(3):159–166, 1949), and the second one, devoted to completeness in type theory (Henkin in J. Symb. Log. 15(2):81–91, 1950). In 1963, Henkin published a completeness proof for propositional type theory (Henkin in J. Symb. Log. 28(3):201–216, 1963), where he devised yet another method not directly based on his completeness proof for the whole theory of types.

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