Degrees of weakly computable reals

Authors:
Keng Meng Ng;Frank Stephan;Guohua Wu
Affiliations:
School of Mathematics, Statistics and Computer Science, Victoria University of Wellington, New Zealand;School of Computing and Department of Mathematics, National University of Singapore, Singapore;School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
Venue:
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Year:
2006

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Abstract

This paper studies the degrees of weakly computable reals. It is shown that certain types of limit-recursive reals are Turing incomparable to all weakly computable reals except the recursive and complete ones. Furthermore, it is shown that an r.e. Turing degree is array-recursive iff every real in it is weakly computable.