# Richard Shore

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]
Richard A. Shore
BornAugust 18, 1946 (age 75)
CitizenshipAmerican
Alma materMIT
Scientific career
FieldsMathematics
InstitutionsCornell University
ThesisPriority Arguments in Alpha-Recursion Theory (1972)
Doctoral advisorGerald E. Sacks

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. 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.