Regular reals | Zendy

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Regular reals

Author(s) -

Wu Guohua

Publication year - 2005

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.200310129

Subject(s) - mathematics , combinatorics , discrete mathematics , set (abstract data type) , hierarchy , computer science , programming language , economics , market economy

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 S n 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: S 1 ⊂ S 2 ⊂ · · · ⊂ S n ⊂ · · · ⊂ ⊂ 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)

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