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ON THE C.E. DEGREES REALIZABLE IN
$\Pi ^0_1$ CLASSES
- Part of
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- Journal:
- The Journal of Symbolic Logic / Volume 89 / Issue 3 / September 2024
- Published online by Cambridge University Press:
- 24 April 2023, pp. 1370-1395
- Print publication:
- September 2024
-
- Article
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- You have access
- Open access
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We study for each computably bounded
$\Pi ^0_1$ 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 
$\Pi ^0_1$ class where all c.e. members have degree a. We also show that every 
$\Pi ^0_1$ set of c.e. indices is realized in some perfect 
$\Pi ^0_1$ class, and classify the sets of c.e. degrees which can be realized in some 
$\Pi ^0_1$ class as exactly those with a computable representation.
