Leon Henkin

Henkin in 1990

Leon Albert Henkin (April 19, 1921, Brooklyn, New York - November 1, 2006, Oakland, California) was an American logician, whose works played a strong role in the development of logic, particularly in the theory of types. He was an active scholar at the University of California, Berkeley, where he made great contributions as a researcher, teacher, as well as in administrative positions.[1] At this university he directed, together with Alfred Tarski, the Group in Logic and the Methodology of Science,[2] from which many important logicians and philosophers emerged. He had a strong sense of social commitment and was a passionate defender of his pacifist and progressive ideas.[2] He took part in many social projects aimed at teaching mathematics, as well as projects aimed at supporting women's and minority groups to pursue careers in mathematics and related fields. A lover of dance and literature, he appreciated life in all its facets: art, culture, science and, above all, the warmth of human relations.[2] He is remembered by his students for his great kindness, as well as for his academic and teaching excellence.[3]

Henkin is mainly known for his completeness proofs of diverse formal systems, such as type theory and first-order logic (the completeness of the latter, in its weak version, had been proven by Kurt Gödel in 1929).[4] To prove the completeness of type theory, Henkin introduces new semantics, not equivalent to standard semantics, based on structures called general models (also known as Henkin models). The change of semantics that he proposed permits to provide a complete deductive calculus for type theory and for second-order logic, amongst other logics. Henkin methods have aided to prove various model theory results, both in classical and non-classical logics. Besides logic, the other branch on which his investigations were centered was algebra; he specialized in cylindric algebras, in which he worked together with Tarski and Donald Monk.[5] As for the philosophy of mathematics, although the works in which he explicitly approaches it are scarce, he can be considered to have a nominalist position.[6]

  1. ^ Wells, Benjamin (2014). «Leon Henkin and a Life of Service». In María Manzano et al., ed. The Life and Work of Leon Henkin. Springer International Publishing. pp. 41-55. ISBN 978-3-319-09718-3. doi:10.1007/978-3-319-09719-0_11.
  2. ^ a b c Manzano, María; Alonso, Enrique (2014). «Leon Henkin». In Manzano et al., María, ed. The Life and Work of Leon Henkin. Springer International Publishing. pp. 3-22. ISBN 978-3-319-09718-3. doi:10.1007/978-3-319-09719-0_11.
  3. ^ In the compilation exhibited in Manzano, María et al., ed. The Life and Work of Leon Henkin. Springer International Publishing. ISBN 978-3-319-09718-3. doi:10.1007/978-3-319-09719-0_11 diverse texts may be found on which the authors share their experiences as Henkin's students.
  4. ^ Gödel, Kurt (1929). «On the completeness of the calculus of logic». In Feferman, S., Dawson, J., Kleene, S., Moore, G., Solovay R., van Heijenoort, J., ed. Kurt Godel: collected works. Vol. 1: Publications 1929-1936. pp. 60-101. ISBN 0-19-503964-5. OCLC 12371326.
  5. ^ Monk, Donald (2014). «Leon Henkin and Cylindric Algebras.». In Manzano et al., ed. The Life and Work of Leon Henkin, Essays on His Contributions (en inglés). Springer International Publishing. pp. 59-66. ISBN 978-3-319-09719-0. doi:10.1007/978-3-319-09719-0_11.
  6. ^ Manzano, María (2014). «Henkin on Completeness». In Manzano et al., ed. The Life and Work of Leon Henkin, Essays on His Contributions. Springer International Publishing. pp. 149-173. ISBN 978-3-319-09719-0. doi:10.1007/978-3-319-09719-0_11.