Richard Shore

Richard Arnold Shore ( born August 18, 1946) is an American mathematical logician who mainly deals with recursion.

Shore received his doctorate in 1972 at the Massachusetts Institute of Technology Gerald E. Sacks (Priority argument in alpha - Recursion Theory), where he was an assistant from 1968. As a post-doc, he was until 1974 Instructor at the University of Chicago, and only then assistant professor, associate professor in 1978 and from 1983 professor at Cornell University. He has been a visiting scientist and visiting professor at Harvard University, the Hebrew University, in Chicago, at MIT, in Singapore, in Siena and at MSRI.

Shore refuted the homogeneity conjecture of Hartley Rogers, by showing that there are Turing degrees a, b, for which the structure of the Turing degrees above a, b ​​is not isomorphic. With Theodore A. Slaman he proved in 1999 that Turing jumps are definable in the structure of the Turing degrees.

He was invited speaker on the ICM in Warsaw 1983 ( The Degrees of Unsolvability: the Ordering of Functions by Relative Computability ). In 2009 he was Godel Lecturer ( Reverse Mathematics: the playground of logic ). 1984 to 1993 he was editor of the Journal of Symbolic Logic, and 1993-2000 of the Bulletin of Symbolic Logic. He is a Fellow of the American Mathematical Society.

Writings

• Anil Nerode: Logic for Applications, Springer 1993
• Alpha- Recursion theory, in Jon Barwise (editor): Handbook of mathematical logic, North Holland 1977, S.653