Richard Arnold Shore (born August 18, 1946) is a professor of mathematics at

Cornell University Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...

who works in

recursion theory Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since ex ...

. He is particularly known for his work on

\mathcal

, the

partial order In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. The word ''partial'' is used to indicate that not every pair of elements needs to be comparable ...

of the

Turing degrees In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natural numbers measures the level of algorithmic unsolvability of the set. Overview The concept of Turing degree is fund ...

. * Shore settled the Rogers homogeneity conjecture by showing that there are Turing degrees

a

and

b

such that

\mathcal_a

and

\mathcal_b

, the structures of the degrees above

a

and

b

respectively, are not isomorphic. * In joint work with

Theodore Slaman Theodore Allen Slaman (born April 17, 1954) is a professor of mathematics at the University of California, Berkeley who works in recursion theory. Slaman and W. Hugh Woodin formulated the Bi-interpretability Conjecture for the Turing degrees, w ...

, Shore showed that the

Turing jump In computability theory, the Turing jump or Turing jump operator, named for Alan Turing, is an operation that assigns to each decision problem a successively harder decision problem with the property that is not decidable by an oracle machine ...

is definable in

\mathcal

Career

He was, in 1983, an

invited speaker at the International Congress of Mathematicians An invitation system is a method of encouraging people to join an organization, such as a Club (organization), club or a website. In regular society, it refers to any system whereby new members are chosen; they cannot simply apply. In relation to w ...

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''). He was an editor from 1984 to 1993 of the

Journal of Symbolic Logic The '' Journal of Symbolic Logic'' is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic. It was established in 1936 and covers mathematical logic. The journal is indexed by '' Mathematical Reviews'', Zent ...

and from 1993 to 2000 of the

Bulletin of Symbolic Logic Bulletin or The Bulletin may refer to: Periodicals (newspapers, magazines, journals) * ''Bulletin'' (online newspaper), a Swedish online newspaper * ''The Bulletin'' (Australian periodical), an Australian magazine (1880–2008) ** Bulletin Deb ...

. In 2012, he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

.List of Fellows of the American Mathematical Society
retrieved 2013-07-18.

References

External links

Cornell Math - Richard A. Shore
*
MathSciNet - Richard A. Shore
Living people American logicians Cornell University faculty Fellows of the American Mathematical Society 20th-century American mathematicians 21st-century American mathematicians 1946 births {{US-mathematician-stub