## WORKING WITH STRONG REDUCIBILITIES ABOVE TOTALLY ω-C.E. DEGREES

Citations: | 3 - 3 self |

### BibTeX

@MISC{Barmpalias_workingwith,

author = {George Barmpalias and Rod Downey and Noam Greenberg},

title = {WORKING WITH STRONG REDUCIBILITIES ABOVE TOTALLY ω-C.E. DEGREES},

year = {}

}

### OpenURL

### Abstract

Abstract. We investigate the connections between the complexity of a c.e. set, as calibrated by its strength as an oracle for Turing computations of functions in the Ershov hierarchy, and how strong reducibilities allows us to compute such sets. For example, we prove that a c.e. degree is totally ω-c.e. iff every set in it is weak truth-table reducible to a hypersimple, or ranked, set. We also show that a c.e. degree is array computable iff every left-c.e. real of that degree is reducible in a computable Lipschitz way to a random left-c.e. real (an Ω-number). 1.