The Turing degrees for some computation model with the real parameter

Abstract

L. Blum, M. Shub and S. Smale defined a kind of computation model having parameters that take real values [2]. In this paper we will extend their computation theory on the basis of the conventional recursion theory which is constructed on the domain of integers. In particular, we will define the Turing degree for the set of reals similarly to the Turing degree for the set of integers, so as to derive some related results.