John Barkley Rosser Sr. (December 6, 1907 – September 5, 1989) was an American logician, a student of Alonzo Church, and known for his part in the Church–Rosser theorem in lambda calculus. He also developed what is now called the "Rosser sieve" in number theory. He was part of the mathematics department at Cornell University from 1936 to 1963, chairing it several times. He was later director of the Army Mathematics Research Center at the University of Wisconsin–Madison and the first director of the Communications Research Division of IDA. Rosser also authored mathematical textbooks.
In 1936, he proved Rosser's trick, a stronger version of Gödel's first incompleteness theorem, showing that the requirement for ω-consistency may be weakened to consistency. Rather than using the liar paradox sentence equivalent to "I am not provable," he used a sentence that stated "For every proof of me, there is a shorter proof of my negation".
In prime number theory, he proved Rosser's theorem.
The Kleene–Rosser paradox showed that the original lambda calculus was inconsistent.
Rosser died of an aneurysm September 5, 1989, at his home in Madison, Wisconsin.
Rosser's son, John Barkley Rosser Jr. (1948–2023), was a mathematical economist and professor at James Madison University in Harrisonburg, Virginia.
1934: A mathematical logic without variables, Univ. Diss. Princeton, NJ, p. 127–150, 328–355
1953: Logic for mathematicians, McGraw-Hill 2nd edition, Chelsea Publ. Co. 1978, 578 p., ISBN 0-8284-0294-9
1969: Simplified Independence Proofs: Boolean Valued Models of Set Theory, Academic Press
1984: "Highlights of the History of Lambda calculus", Annals of the History of Computing 6(4): 337–349
See Barkley Rosser papers at University of Texas
J. Barkley Rosser at the Mathematics Genealogy Project
Interview with Rosser and Stephen Kleene about their experiences at Princeton