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Journal of Logic and Computation

Volume 13, Issue 2, April 2003: pp. 159-172

On the Turing Degrees of Weakly Computable Real Numbers

Xizhong Zheng1

1Theoretische Informatik, BTU Cottbus, 03044 Cottbus, Germany. E-mail: zheng@informatik.tu-cottbus.de

The Turing degree of a real number x is defined as the Turing degree of its binary expansion. This definition is quite natural and robust. In this paper we discuss some basic degree properties of semi-computable and weakly computable real numbers introduced by Weihrauch and Zheng. We show that there are two real numbers of c.e. binary expansions such that their difference does not have an [ohgr].c.e. Turing degree.

Keywords: Weakly computable real number; Turing degree of real number

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