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Theodore Allen Slaman
is a professor of mathematics at the University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
who works in 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...
Slaman and W. Hugh Woodin
William Hugh Woodin is an American mathematician and set theorist at University of California, Berkeley. He has made many notable contributions to the theory of inner models and determinacy. A type of large cardinal, the Woodin cardinal, bears his name.-Biography:Born in Tucson, Arizona, Woodin...
formulated the Bi-interpretability Conjecture for the Turing degrees, which conjectures that the partial order of the Turing degrees is logically equivalent
In logic, statements p and q are logically equivalent if they have the same logical content.Syntactically, p and q are equivalent if each can be proved from the other...
to second order arithmetic. They showed that the Bi-interpretability Conjecture is equivalent to there being no nontrivial automorphism of the Turing degrees. They also exhibited limits on the possible automorphisms of the Turing degrees by showing that any automorphism will be arithmetically definable.