Extending properly n - REA sets1

• Published in: Computability Vol. 11; no. 3-4; pp. 241 - 267
• Main Authors: Cholak, Peter, Gerdes, Peter
• Format: Journal Article
• Language: English
• Published: 21.12.2022

In 1982, Soare and Stob proved that if A is an r.e. set which isn’t computable then there is a set of the form A ⊕ W e which isn’t of r.e. Turing degree. If we define a properly n + 1-REA set to be an n + 1-REA set which isn’t Turing equivalent to any n-REA set this result shows that every properly...