William Alvin Howard

William Alvin Howard (* 1926 ) is an American mathematical logician.

Howard received his PhD in 1956 from the University of Chicago with Saunders MacLane and André Weil (k-fold recursion and well-ordering). He was a professor at Pennsylvania State University in the 1960s and then at the University of Illinois at Chicago . He is a fellow of the American Mathematical Society .

Howard showed with Haskell Curry (in works that go back to the 1930s) an analogy ( Curry-Howard isomorphism ) between intuitionist logic and lambda calculus . He also introduced the Howard ordinal numbers named after him (or Bachmann-Howard ordinal numbers after him and Heinz Bachmann ), which are defined in proof theory.

Fonts

• The formulas-as-types notion of construction, manuscript from 1969, in Jonathan Seldin, Roger Hindley (editor): To HB Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, Boston, Academic Press 1980, p. 479 ( Curry Howard Correspondence)
• A system of abstract constructive ordinals, Journal of Symbolic Logic, Vol. 37 1972, pp. 355-374 (Bachmann-Howard ordinal numbers)

Web links

• William Alvin Howard in the Mathematics Genealogy Project (English)