John Barkley Rosser Sr. (December 6, 1907 – September 5, 1989) was an American

logician Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

, a student of

Alonzo Church Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician, computer scientist, logician, philosopher, professor and editor who made major contributions to mathematical logic and the foundations of theoretical computer scien ...

, and known for his part in the

Church–Rosser theorem In lambda calculus, the Church–Rosser theorem states that, when applying reduction rules to terms, the ordering in which the reductions are chosen does not make a difference to the eventual result. More precisely, if there are two distinct red ...

, in lambda calculus. He also developed what is now called the " Rosser sieve", in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mat ...

. He was part of the mathematics department at

Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to tea ...

from 1936 to 1963, chairing it several times. He was later director of the Army Mathematics Research Center at the

University of Wisconsin–Madison A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United Stat ...

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 In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the truth ...

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 In number theory, Rosser's theorem states that the ''n''th prime number is greater than n \log n , where \log is the natural logarithm function. It was published by J. Barkley Rosser in 1939. Its full statement is: Let ''p'n'' be the ''n''th ...

. The

Kleene–Rosser paradox In mathematics, the Kleene–Rosser paradox is a paradox that shows that certain systems of formal logic are inconsistent, in particular the version of Haskell Curry's combinatory logic introduced in 1930, and Alonzo Church's original lambda ca ...

showed that the original lambda calculus was inconsistent. Rosser died of an

aneurysm An aneurysm is an outward bulging, likened to a bubble or balloon, caused by a localized, abnormal, weak spot on a blood vessel wall. Aneurysms may be a result of a hereditary condition or an acquired disease. Aneurysms can also be a nidus ( ...

September 5, 1989, at his home in

Madison, Wisconsin Madison is the county seat of Dane County and the capital city of the U.S. state of Wisconsin. As of the 2020 census the population was 269,840, making it the second-largest city in Wisconsin by population, after Milwaukee, and the 80th-lar ...

. 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; 2nd ed., Chelsea Publ. Co. 1978, 578 p., * ''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 * Se
''Barkley Rosser papers''
for a complete list of Rosser's publications.

References

External links

*

{{DEFAULTSORT:Rosser, J. Barkley 1907 births 1989 deaths People from Jacksonville, Florida American logicians 20th-century American mathematicians Princeton University alumni Cornell University faculty University of Wisconsin–Madison faculty Presidents of the Society for Industrial and Applied Mathematics