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Limit lemmas and jump inversion in the enumeration degrees

Limit lemmas and jump inversion in the enumeration degrees We show that there is a limit lemma for enumeration reducibility to 0 e ', analogous to the Shoenfield Limit Lemma in the Turing degrees, which relativises for total enumeration degrees. Using this and `good approximations' we prove a jump inversion result: for any set W with a good approximation and any set X< e W such that W≤ e X' there is a set A such that X≤ e A< e W and A'=W'. (All jumps are enumeration degree jumps.) The degrees of sets with good approximations include the Σ0 2 degrees and the n-CEA degrees. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Limit lemmas and jump inversion in the enumeration degrees

Griffiths, Evan J.
Archive for Mathematical Logic , Volume 42 (6) – Mar 7, 2003
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References (8)

Publisher
Springer Journals
Copyright
Copyright © 2003 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s00153-002-0161-z
Publisher site
See Article on Publisher Site

Abstract

We show that there is a limit lemma for enumeration reducibility to 0 e ', analogous to the Shoenfield Limit Lemma in the Turing degrees, which relativises for total enumeration degrees. Using this and `good approximations' we prove a jump inversion result: for any set W with a good approximation and any set X< e W such that W≤ e X' there is a set A such that X≤ e A< e W and A'=W'. (All jumps are enumeration degree jumps.) The degrees of sets with good approximations include the Σ0 2 degrees and the n-CEA degrees.

Journal

Archive for Mathematical Logic – Springer Journals

Published: Mar 7, 2003

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