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**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.^{[1]} 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.

John Barkley Rosser | |
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Born | Jacksonville, Florida, U.S. | December 6, 1907

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

Alma mater | Princeton University |

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

Scientific career | |

Fields | Mathematical logic Number theory |

Institutions | Cornell University University of Wisconsin–Madison, IDA/CRD |

Thesis | A Mathematical Logic without Variables (1934) |

Doctoral advisor | Alonzo Church |

Doctoral students | George E. Collins Elliott Mendelson Gerald Sacks |

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.^{[2]}^{[1]}

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

*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.

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^{a}^{b}"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 **^**"Deaths",*Washington Post*, September 19, 1989, archived from the original on November 3, 2012**^**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.

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