Low basis theorem

Low basis theorem

The low basis theorem in computability theory states that every nonempty Pi^0_1 class contains a set of low degree. It was first proved by Carl Jockusch and Robert I. Soare in 1972.

References

*Soare, R. "Recursively enumerable sets and degrees." Perspectives in Mathematical Logic. Springer-Verlag, Berlin, 1987. ISBN 3-540-15299-7
*CG Jockusch, Jr and RI Soare, "Π(0, 1) Classes and Degrees of Theories" in Transactions of the American Mathematical Society (1972). [http://links.jstor.org/sici?sici=0002-9947(197211)173%3C33%3ACADOT%3E2.0.CO%3B2-O ]


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