J. Barkley Rosser
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J. Barkley Rosser
John Barkley Rosser
Born December 6, 1907
Jacksonville, Florida, U.S.
Died September 5, 1989 (aged 81)
Nationality United States
Alma mater Princeton University
Known for Church–Rosser theorem
Rosser's sieve
Scientific career
Fields Mathematical logic
Number theory
Doctoral students Elliott Mendelson
Gerald Sacks

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 later director of the Army Mathematics Research Center at the University of Wisconsin-Madison. 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 ?-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.[1][2]

Rosser's son, John Barkley Rosser, Jr., is a mathematical economist and professor at James Madison University in Harrisonburg, Virginia.

## Selected publications

• A mathematical logic without variables by John Barkley Rosser, Univ. Diss. Princeton, NJ 1934, p. 127-150, 328-355
• Logic for mathematicians by John B. Rosser, McGraw-Hill 1953;[3] 2nd ed., Chelsea Publ. Co. 1978, 578 p., ISBN 0-8284-0294-9
• Highlights of the History of Lambda calculus, by J. Barkley Rosser, Annals of the History of Computing, 1984, vol 6, n 4, pp. 337-349
• Simplified Independence Proofs: Boolean Valued Models of Set Theory, by J. Barkley Rosser, Academic Press, 1969
• See Barkley Rosser papers for a complete list of Rosser's publications.

## References

1. ^ "Deaths", Washington Post, September 19, 1989
2. ^ "Memorial Resolution on the Death of Emeritus Professor J. Barkley Rosser" (PDF), University of Wisconsin, Madison, March 5, 1990, archived from the original (PDF) on June 8, 2011
3. ^ Curry, H. B. (1954). "Review: Logic for mathematicians by J. B. Rosser" (PDF). Bull. Amer. Math. Soc. 60 (3): 266-272. doi:10.1090/s0002-9904-1954-09798-7.