Richard Shore

Richard A. Shore
Born	August 18, 1946
Citizenship	United States
Fields	Mathematics
Institutions	Cornell University
Alma mater	MIT
Doctoral advisor	Gerald E. Sacks

Richard A. 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]

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. doi:10.1073/pnas.76.9.4218. JSTOR 70054. PMC 411543. PMID 16592707. http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=411543.
^ Shore, R.A.; Slaman, T.A. (1999). "Defining the Turing jump". Math. Res. Lett 6 (5–6): 711–722. http://www.mrlonline.org/mrl/1999-006-006/1999-006-006-010.pdf. Retrieved 2008-07-14.

External links

Cornell Math - Richard A. Shore.

Richard Shore at the Mathematics Genealogy Project.

Persondata
Name	Shore, Richard
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Date of birth	August 18, 1946
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