Leon Henkin is a logician, currently Emeritus Professor at Berkeley. He is principally known for the "Henkin Completeness Proof": his version of the proof of the semantic completeness of standard systems of first-order logic.

Henkin's result was not novel — it had first been proved by Kurt Gödel in his doctoral dissertation which was completed in 1929. (See Gödel's completeness theorem. Gödel published a version of the proof in 1930.) Henkin's proof is much easier to survey than Gödel's and has thus become the standard choice of completeness proof for presentation in introductory classes and texts.

It is non-constructive (a pure existence proof): while it assures you that if a sentence α follows (semantically) from a set of sentences Σ, then there is a proof of α from Σ, it gives no indication of the nature of that proof.

References

Henkin, Leon. 1949. "The Completeness of the First-Order Functional Calculus", Journal of Symbolic Logic. 14: 159-166.