Limit lemmas and jump inversion in the enumeration degrees

Archive for Mathematical Logic 42 (6):553-562 (2003)
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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

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Citations of this work

Density of the cototal enumeration degrees.Joseph S. Miller & Mariya I. Soskova - 2018 - Annals of Pure and Applied Logic 169 (5):450-462.
Goodness in the enumeration and singleton degrees.Charles M. Harris - 2010 - Archive for Mathematical Logic 49 (6):673-691.
Avoiding uniformity in the Δ 2 0 enumeration degrees.Liliana Badillo & Charles M. Harris - 2014 - Annals of Pure and Applied Logic 165 (9):1355-1379.
On the jump classes of noncuppable enumeration degrees.Charles M. Harris - 2011 - Journal of Symbolic Logic 76 (1):177 - 197.

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References found in this work

Then-rea enumeration degrees are dense.Alistair H. Lachlan & Richard A. Shore - 1992 - Archive for Mathematical Logic 31 (4):277-285.
Jumps of quasi-minimal enumeration degrees.Kevin McEvoy - 1985 - Journal of Symbolic Logic 50 (3):839-848.
On minimal pairs of enumeration degrees.Kevin McEvoy & S. Barry Cooper - 1985 - Journal of Symbolic Logic 50 (4):983-1001.
The $\Pi^0_2$ Enumeration Degrees are Not Dense.William Calhoun & Theodore Slaman - 1996 - Journal of Symbolic Logic 61 (3):1364-1379.

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