Richard Shore

Richard A. Shore

Born	August 18, 1946 (1946-08-18) (age 71)
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 (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 ${\mathcal {D}}$ , 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

↑ Shore, R.A. (1979). "The homogeneity conjecture". Proceedings of the National Academy of Sciences of the United States of America. 76 (9): 4218–4219. JSTOR 70054. PMC 411543 . PMID 16592707. doi:10.1073/pnas.76.9.4218.
↑ Shore, R.A.; Slaman, T.A. (1999). "Defining the Turing jump" (PDF). Math. Res. Lett. 6 (5–6): 711–722. Retrieved 2008-07-14.
↑ Gödel Lectures, Association for Symbolic Logic
↑ List of Fellows of the American Mathematical Society, retrieved 2013-07-18.

External links

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.