Jeff Paris
Jeffrey Bruce Paris (* 1944 ) is a British mathematician who studies mathematical logic. He is a professor at the University of Manchester , where he received his doctorate from Robin Gandy in 1969 ( Boolean extensions and large cardinals ).
Live and act
He became known through the Paris-Harrington theorem of 1977 with Leo Harrington , in which the non-provability of a true theorem of elementary arithmetic from the Peano axioms of arithmetic was shown for the first time . The existence of such true but unprovable propositions was generally known for (sufficiently rich) formal systems according to Gödel's incompleteness theorem , but Paris and Harrington provided for the first time an elementary example that came from the Ramsey theory . In 1982, together with Laurie Kirby , he showed that Goodstein's theorem could not be proven with methods of Peano arithmetic (theorem of Kirby and Paris).
In 1983 he received the Whitehead Prize . In 1999 he was elected to the British Academy .
Fonts
- The uncertain reasoner's companion: a mathematical perspective , Cambridge University Press, 1994, ISBN 0-521-46089-1
Web links
- Professor Jeff B. Paris - Homepage at the University of Manchester
- Eric W. Weisstein : Natural Independence Phenomenon . In: MathWorld (English).
References
- ^ Jeff Paris, Leo Harrington: A Mathematical Incompleteness in Peano Arithmetic . In Jon Barwise (editor): Handbook of Mathematical Logic , North-Holland, Amsterdam 1977, pp. 1133-1142
- ↑ also shown in Craig Smoryński: Some rapidly growing functions , Mathematical Intelligencer 2, 1979/80, pp. 149-154
- ↑ Laurie Kirby, Jeff Paris: Accessible independence results for Peano Arithmetic , Bulletin London Mathematical Society 14, 1982, pp. 285-293
| personal data | |
|---|---|
| SURNAME | Paris, Jeff |
| ALTERNATIVE NAMES | Paris, Jeffrey Bruce (full name) |
| BRIEF DESCRIPTION | British mathematician |
| DATE OF BIRTH | 1944 |