A c.e. real that cannot be sw-computed by any Omega number

A c.e. real that cannot be sw-computed by any $\Omega$ number

G. Barmpalias

Summary

The strong weak truth table (sw) reducibility was suggested by Downey, Hirschfeldt, and LaForte as a measure of relative randomness, alternative to the Solovay reducibility. It also occurs naturally in proofs in classical computability theory as well as in the recent work of Soare, Nabutovsky and Weinberger on applications of computability to differential geometry. We study the sw-degrees of c.e. reals and con- struct a c.e. real which has no random c.e. real (i.e. Chaitin's $\Omega$ number) sw-above it. A.