| Abstract: | Say that α is an n‐strongly c. e. (n‐strongly computably enumerable) real if α is a sum of n many strongly c. e. reals, and that α is regular if α is n‐strongly c. e. for some n. Let Sn be the set of all n‐strongly c. e. reals, Reg be the set of regular reals and CE be the set of c. e. reals. Then we have: S1 ? S2 ? · · · ? Sn ? · · · ? ? Reg ? CE . This gives a hierarchy of the c. e. reals. We also study the regularity of the d. c. e. reals. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
