Theodore Allen Slaman (born April 17, 1954) is a professor of mathematics at the
University of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...
who works in
recursion theory
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has sinc ...
.
Slaman and
W. Hugh Woodin
William Hugh Woodin (born April 23, 1955) is an American mathematician and set theorist at Harvard University. He has made many notable contributions to the theory of inner models and determinacy. A type of large cardinals, the Woodin cardinals, ...
formulated the Bi-interpretability Conjecture for the
Turing degrees, which conjectures that the
partial order
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a bina ...
of the Turing degrees is
logically equivalent
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...
to
second-order arithmetic
In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets. It is an alternative to axiomatic set theory as a foundation for much, but not all, of mathematics.
A precur ...
. 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.
References
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External links
home page
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Living people
American logicians
20th-century American mathematicians
21st-century American mathematicians
University of California, Berkeley faculty
Harvard University alumni
1954 births
Gödel Lecturers
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