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.
• In joint work with Theodore Slaman, Shore showed that the Turing jump is definable in ${\displaystyle {\mathcal {D}}}$.