Computability in Europe 2006
Logical Approaches to Computational Barriers

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Special Session Talk:
A Computability Theory of Real Numbers

Speaker: Xizhong Zheng

Abstract

In mathematics, various representations of real numbers have been
investigated.
Their standard effectivizations lead to equivalent definitions of
computable
real numbers. For the primitive recursive level, however,  these
effectivizations are not equivalent any more. Similarly, if the weaker
computability is considered, we usually obtain different weak
computability
notions of reals according to different representations of real number. In
this
paper we summarize several recent results about weak computability of real
numbers and their hierarchies. 


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