The recursively enumerable degrees have infinitely many one-types (Q1823931)

The authors prove the following theorem: There exist r.e. degrees \(\{c_ m\}_{m\in \omega}\) such that for all m: (i) \(c_ m>0\); (ii) \(c_ m\) does not bound a minimal pair; (iii) for every \(n\neq m\), \(c_ m\) and \(c_ n\) form a minimal pair. Applications and an informal motivation are also included. This is a deep mathematical paper which should be of great value for many ``practically oriented'' computer scientists.