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**William Alvin Howard** (born 1926) is a proof theorist best known for his work demonstrating formal similarity between intuitionistic logic and the simply typed lambda calculus that has come to be known as the Curry–Howard correspondence. He has also been active in the theory of proof-theoretic ordinals. He earned his Ph.D. at the University of Chicago in 1956 for his dissertation "k-fold recursion and well-ordering".^{[1]} He was a student of Saunders Mac Lane.

The Howard ordinal (also known as the Bachmann–Howard ordinal) was named after him.

He was the first to carry out an ordinal analysis of the intuitionistic theory of inductive definitions.^{[2]}^{p.27}

He was elected to the 2018 class of fellows of the American Mathematical Society.^{[3]}

**^**"Holdings: k-fold recursion and well-ordering". The University of Chicago Library Catalog. Retrieved 2015-05-04.**^**M. Rathjen, "Proof Theory: From arithmetic to set theory". Accessed 22 February 2024.**^***2018 Class of the Fellows of the AMS*, American Mathematical Society, retrieved 2017-11-03

- Entry for
*William Alvin Howard*at the Mathematics Genealogy Project. - Howard, W. A.; Kreisel, G. (September 1966). "Transfinite Induction and Bar Induction of Types Zero and One, and the Role of Continuity in Intuitionistic Analysis".
*The Journal of Symbolic Logic*.**3**(3). Association for Symbolic Logic: 325–358. doi:10.2307/2270450. JSTOR 2270450. S2CID 5683782.