{{Short description|American logician (1907–1989)}} {{Infobox scientist |name = John Barkley Rosser |image = |image_size = |caption = |workplaces = [[Cornell University]]<br/>[[University of Wisconsin–Madison]], [[Institute for Defense Analyses#Center for Communications and Computing|IDA/CRD]] |birth_date = {{birth date|1907|12|06}} |birth_place = [[Jacksonville, Florida]], U.S. |death_date = {{death date and age|1989|09|05|1907|12|06}} |death_place = [[Madison, Wisconsin]], U.S. |fields = [[Mathematical logic]]<br/>[[Number theory]] |alma_mater = [[Princeton University]] |thesis_title = A Mathematical Logic without Variables |thesis_year = 1934 |doctoral_advisor = [[Alonzo Church]] |doctoral_students = [[George E. Collins]]<br/> [[Elliott Mendelson]]<br/> [[Gerald Sacks]] |known_for = [[Church–Rosser theorem]]<br/>[[Kleene–Rosser paradox]]<br/>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 part of the mathematics department at [[Cornell University]] from 1936 to 1963, chairing it several times.<ref name="wisc-mem"/> He was later director of the Army Mathematics Research Center at the [[University of Wisconsin–Madison]] and the first director of the [[Institute for Defense Analyses#Center for Communications and Computing|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]] 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]].<ref>{{Citation |url=http://www.highbeam.com/doc/1P2-1212612.html |archive-url=https://web.archive.org/web/20121103074821/http://www.highbeam.com/doc/1P2-1212612.html |url-status=dead |archive-date=November 3, 2012 |title=Deaths |newspaper=[[Washington Post]] |date=September 19, 1989 }}</ref><ref name="wisc-mem">{{Citation |url=http://www.cs.wisc.edu/news/rosser.memorial.pdf |title=Memorial Resolution on the Death of Emeritus Professor J. Barkley Rosser |work=University of Wisconsin, Madison |date=March 5, 1990 |archiveurl=https://web.archive.org/web/20110608075258/http://www.cs.wisc.edu/news/rosser.memorial.pdf |archivedate=June 8, 2011}}</ref>
Rosser's son, [[J. Barkley Rosser Jr.|John Barkley Rosser Jr.]] (1948–2023), was a [[Mathematical economics|mathematical economist]] and professor at James Madison University in Harrisonburg, Virginia.
==Selected publications== * 1934: ''A mathematical logic without variables'', Univ. Diss. Princeton, NJ, p. 127–150, 328–355 * 1953: ''Logic for mathematicians'', [[McGraw-Hill]]<ref>{{cite journal|author=Curry, H. B.|authorlink=Haskell Curry|title=Review: ''Logic for mathematicians'' by J. B. Rosser|journal=[[Bulletin of the American Mathematical Society]] |year=1954|volume=60|issue=3|pages=266–272|url=https://www.ams.org/journals/bull/1954-60-03/S0002-9904-1954-09798-7/S0002-9904-1954-09798-7.pdf|doi=10.1090/s0002-9904-1954-09798-7|doi-access=free}}</ref> 2nd edition, Chelsea Publ. Co. 1978, 578 p., {{ISBN|0-8284-0294-9}} * 1969: ''Simplified Independence Proofs: Boolean Valued Models of Set Theory'', [[Academic Press]] * 1984: "Highlights of the History of Lambda calculus", ''[[Annals of the History of Computing]]'' 6(4): 337–349 * See [http://www.lib.utexas.edu/taro/utcah/00212/cah-00212.html ''Barkley Rosser papers''] at [[University of Texas]]
==References== {{Reflist}}
==External links== *{{MathGenealogy|id=8013}} *[https://web.archive.org/web/20020308033648/http://infoshare1.princeton.edu/libraries/firestone/rbsc/finding_aids/mathoral/pm02.htm Interview with Rosser and Stephen Kleene about their experiences at Princeton]
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{{DEFAULTSORT:Rosser, J. Barkley}} [[Category:1907 births]] [[Category:1989 deaths]] [[Category:People from Jacksonville, Florida]] [[Category:American logicians]] [[Category:20th-century American mathematicians]] [[Category:Princeton University alumni]] [[Category:Cornell University faculty]] [[Category:University of Wisconsin–Madison faculty]] [[Category:Presidents of the Society for Industrial and Applied Mathematics]]