Isolated d.c.e. degrees and $\hat{I}{\pounds }_1$ induction

Yiqun Liu, Yong Liu, Cheng Peng

A Turing degree is d.c.e. if it contains a set that is the difference of two c.e. sets. A d.c.e. degree $\mathbf{d}$ is isolated by a c.e. degree $\mathbf{a}<\mathbf{d}$ if all c.e…