# J. Barkley Rosser

John Barkley Rosser | |
---|---|

Born |
Jacksonville, Florida, U.S. | December 6, 1907

Died |
September 5, 1989 81) Madison, Wisconsin, U.S. | (aged

Nationality | United States |

Fields |
Mathematical logic Number theory |

Alma mater | Princeton University |

Doctoral advisor | Alonzo Church |

Doctoral students |
George Collins Theodore Hailperin Walter Joel Harrington Elliott Mendelson Stephen Orey George William Petznick, Jr. Gerald Sacks David Edward Schroer |

Known for |
Church–Rosser theorem Kleene–Rosser paradox Rosser's sieve |

**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 which shows 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.^{[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-
*Highlight 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

- ↑ "Deaths",
*Washington Post*, September 19, 1989 - ↑ "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 - ↑ 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.

## External links

- J. Barkley Rosser at the Mathematics Genealogy Project
- Interview with Rosser and Stephen Kleene about their experiences at Princeton