Richard Shore
Encyclopedia
Richard A. Shore is a professor of mathematics at Cornell University
who works in recursion theory
. He is particularly known for his work on
, the partial order of the Turing degrees.
Cornell University
Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
who works in recursion theory
Recursion theory
Computability theory, also called recursion theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability and definability...
. He is particularly known for his work on
, the partial order of the Turing degrees.- Shore settled the Rogers Homogeneity Conjecture by showing that there are Turing degrees
and 
such that 
and 
, the structures of the degrees above 
and 
respectively, are not isomorphic. - In joint work with Theodore SlamanTheodore SlamanTheodore Allen Slaman 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, which conjectures that the partial order of the Turing degrees is logically...
, Shore showed that the Turing jumpTuring jumpIn 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 with an oracle for .The operator is called a jump...
is definable in
.