ABSTRACT
We see that rAT-reducibility shares many of the nice structural properties of S-reducibility on the c.e. reals while still being a reasonable reducibility on non-c.e. reals. Together with its various characterizations, especially the one in terms of relative K -complexity of initial segments, this makes rK -reducibility a tool with great potential in the study of the relative randomness of reals. As one would expect, little else is known about the structure of rK degrees.
