Carl Jockusch
Encyclopedia
Carl Groos Jockusch, Jr. is an American
mathematician
. He is a professor emeritus at the University of Illinois at Urbana-Champaign
. In 1972 Jockusch and Robert I. Soare
proved the Low Basis Theorem
, an important result in mathematical logic with applications to recursion theory
and reverse mathematics
.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He is a professor emeritus at the University of Illinois at Urbana-Champaign
University of Illinois at Urbana-Champaign
The University of Illinois at Urbana–Champaign is a large public research-intensive university in the state of Illinois, United States. It is the flagship campus of the University of Illinois system...
. In 1972 Jockusch and Robert I. Soare
Robert I. Soare
Robert Irving Soare is an American mathematician. He is currently the Paul Snowden Russell Distinguished Service Professor of Mathematics and Computer Science at the University of Chicago, where he has been on the faculty since 1967...
proved the Low Basis Theorem
Low basis theorem
The low basis theorem in computability theory states that every nonempty \Pi^0_1 class of 2^\omega contains a set of low degree. It was first proved by Carl Jockusch and Robert I. Soare in 1972.- References :...
, an important result in mathematical logic with applications to 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...
and reverse mathematics
Reverse mathematics
Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining method can briefly be described as "going backwards from the theorems to the axioms", in contrast to the ordinary mathematical practice of...
.