$ON THE C.E. DEGREES REALIZABLE IN $\Pi ^0_1$ CLASSES$

ON THE C.E. DEGREES REALIZABLE IN $\Pi ^0_1$ CLASSES

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 realiz...

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Veröffentlicht in:	The Journal of symbolic logic 2024-09, Vol.89 (3), p.1370-1395
Hauptverfasser:	Csima, Barbara F, Downey, Rod, KENG MENG NG
Format:	Artikel
Sprache:	eng
Online-Zugang:	Volltext
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Zusammenfassung:	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.
ISSN:	0022-4812 1943-5886
DOI:	10.1017/jsl.2023.26

Zusammenfassung:	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.
ISSN:	0022-4812 1943-5886
DOI:	10.1017/jsl.2023.26

ON THE C.E. DEGREES REALIZABLE IN \(\Pi ^0_1\) CLASSES