Regular reals

Mathematical Logic Quarterly 51 (2):111-119 (2005)
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Say that α is an n-strongly c. e. 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



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