Richard Shore

Richard A. Shore
Born	August 18, 1946
Citizenship	United States
Fields	Mathematics
Institutions	Cornell University
Alma mater	MIT
Thesis	Priority Arguments in Alpha-Recursion Theory
Doctoral advisor	Gerald E. Sacks

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

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

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" (PDF). Math. Res. Lett 6 (5–6): 711–722. Retrieved 2008-07-14.
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