J. Barkley Rosser

Infobox Scientist
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name = John Barkley Rosser


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birth_date = 1907
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death_date = 1989
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citizenship = USA
nationality = USA
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fields = Mathematical logic
Number theory
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alma_mater = Princeton University
doctoral_advisor = Alonzo Church
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doctoral_students = George Collins
Stephen Orey
Gerald Sacks
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known_for = Kleene-Rosser paradox Rosser's sieve
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John Barkley Rosser Sr. (1907–1989) 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 wrote mathematical textbooks as well.

In 1936, he proved 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's son, John Barkley Rosser, Jr., is known as a mathematical economist and is a professor at James Madison University in Harrisonburg, Virginia.

Writings by Rosser

*"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, 2nd ed., Chelsea Publ. Co. 1978, 578 p., ISBN 0-8284-0294-9
*See [http://www.lib.utexas.edu/taro/utcah/00212/cah-00212.html "Barkley Rosser papers"] for a complete list of Rosser's publications.

External links

*MathGenealogy|id=8013
* [http://infoshare1.princeton.edu/libraries/firestone/rbsc/finding_aids/mathoral/pm02.htm Interview with Rosser and Stephen Kleene about their experiences at Princeton]