ABSTRACT

Before we turn to the structure of the Solovay degrees of c.e. reals, we mention that we know of no characterization of this (or any of the other reducibilities we examine) in terms of test sets. What we are thinking here is that a < /? iff every test failed by /? is failed by a , or something. This, of course is not correct since a and /? will no doubt be different rational intervals. But there should be some computable map, perhaps from test sets to test sets, like an m -reduction which will be along these lines.7