k Leon Albert Henkin19.04.1921–1.11.2006 was an Ameri-can logician and mathematician, best known for the Henkin Completeness Proof for axiomatic deductive systems of first-order logic..
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Leon Albert Henkin(19.04.1921–1.11.2006) was an
Ameri-can logician and mathematician, best known for the Henkin Completeness Proof for axiomatic deductive systems of first-order logic This proof is much simpler and intuitive than the original Gödel proofs, and has become the standard method for semantic completeness proofs since then
After studying mathematics and philosophy at Columbia Col-lege, Henkin was a doctoral student of Alonzo Church at Prince-ton University, where he received his PhD in 1947 He then became Professor of Mathematics at the University of Califor-nia, Berkeley in 1953 where he worked until his retirement in 1991 He was a col-laborator of Alfred Tarski and a keen popularizer of logic and of mathematics
In his doctoral dissertation The completeness of formal systems, Henkin
origi-nally proved the completeness of Church’s higher-order logic using the now-called
general Henkin semantics, where the higher types are interpreted not by the full
space of functions but by a suitably rich subset of it He then adapted his method
to obtain a new completeness proof for first-order logic, introducing the now-called
Henkin constants and Henkin models His proof method is now used for
complete-ness proofs of a wide variety of logical systems Henkin also studied extensions of
first-order logic with branching quantifiers and with infinite strings of quantifiers and proposed game-theoretic semantics for them.
Henkin was not only a distinguished academic and promoter of logic and math-ematics, but also a passionate social activist, instrumental in designing special pro-grams and scholarships for talented students from disadvantaged minorities