Richard Shore

For the English cricketer and British Army officer, see Richard Shore (cricketer).

Richard A. Shore
Born	August 18, 1946 (1946-08-18) (age 78)
Citizenship	American
Alma mater	MIT
Scientific career
Fields	Mathematics
Institutions	Cornell University
Thesis	Priority Arguments in Alpha-Recursion Theory  (1972)
Doctoral advisor	Gerald E. Sacks

Richard Arnold Shore (born August 18, 1946) is a professor of mathematics at Cornell University who works in recursion theory. He is particularly known for his work on ${\displaystyle {\mathcal {D}}}$, the partial order of the Turing degrees.

• Shore settled the Rogers homogeneity conjecture by showing that there are Turing degrees ${\displaystyle a}$ and ${\displaystyle b}$ such that ${\displaystyle {\mathcal {D}}_{a}}$ and ${\displaystyle {\mathcal {D}}_{b}}$, the structures of the degrees above ${\displaystyle a}$ and ${\displaystyle b}$ respectively, are not isomorphic. ^[1]
• In joint work with Theodore Slaman, Shore showed that the Turing jump is definable in ${\displaystyle {\mathcal {D}}}$. ^[2]

Career

He was, in 1983, an invited speaker at the International Congress of Mathematicians in Warsaw and gave a talk The Degrees of Unsolvability: the Ordering of Functions by Relative Computability. In 2009, he was the Gödel Lecturer (Reverse mathematics: the playground of logic). ^[3] He was an editor from 1984 to 1993 of the Journal of Symbolic Logic and from 1993 to 2000 of the Bulletin of Symbolic Logic. In 2012, he became a fellow of the American Mathematical Society. ^[4]

References

1. Shore, R.A. (1979). "The homogeneity conjecture". Proceedings of the National Academy of Sciences of the United States of America . 76 (9): 4218–4219. Bibcode:1979PNAS...76.4218S. doi: 10.1073/pnas.76.9.4218 . JSTOR   70054. PMC   411543 . PMID   16592707.
2. Shore, R.A.; Slaman, T.A. (1999). "Defining the Turing jump". Math. Res. Lett. 6 (5–6): 711–722. doi: 10.4310/MRL.1999.v6.n6.a10 .
3. Gödel Lectures, Association for Symbolic Logic
4. List of Fellows of the American Mathematical Society, retrieved 2013-07-18.

External links

• Cornell Math - Richard A. Shore.
• Richard Shore at the Mathematics Genealogy Project
• MathSciNet - Richard A. Shore