Bounded Computable Enumerability and Hierarchy of Computably Enumerable Reals

  • Xizhong Zheng
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4598)


The computable enumerability (c.e., for short) is one of the most important notion in computability theory and is regarded as the first weakening of the computability. In this paper, we explore further possible weakening of computable enumerability. By restricting numbers of possible big jumps in an increasing computable sequence of rational numbers which converges to a c.e. real number we introduce the notion of h-bounded c.e. reals and then shown that it leads naturally to an Ershov-style hierarchy of c.e. reals. However, the similar idea does not work for c.e. sets. We show that there is a computability gap between computable reals and the reals of c.e. binary expansions.


c.e. sets c.e. reals bounded c.e. reals Ershov’s Hierarchy 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Xizhong Zheng
    • 1
    • 2
  1. 1.Department of Computer Science, Jiangsu University, Zhenjiang 212013China
  2. 2.Theoretische Informatik, BTU Cottbus, D-03044 CottbusGermany

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