On the C.E. degrees realizable in II⁰₁ classes

On the C.E. degrees realizable in II⁰₁ classes

We study for each computably bounded Π01 class P the set of degrees of c.e. paths in P. We show, amongst other results, that for every c.e. degree a there is a perfect Π01 class where all c.e. members have degree a. We also show that every Σ03 set of c.e. indices is realized in some perfect Π01 clas...

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Bibliographic Details
Main Authors: Csima, Barbara F., Downey, Rod, Ng, Keng Meng
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2023
Subjects:
Science::Mathematics
Effectively Closed Sets
Computably Enumerable Degrees
Online Access:https://hdl.handle.net/10356/171806
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Institution: Nanyang Technological University
Language: English
Description
Summary:We study for each computably bounded Π01 class P the set of degrees of c.e. paths in P. We show, amongst other results, that for every c.e. degree a there is a perfect Π01 class where all c.e. members have degree a. We also show that every Σ03 set of c.e. indices is realized in some perfect Π01 class, and classify the sets of c.e. degrees which can be realized in some Π01 class as exactly those with a computable representation.

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