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A HIERARCHY OF COMPUTABLY ENUMERABLE DEGREES

Published online by Cambridge University Press:  26 April 2018

ROD DOWNEY  and
NOAM GREENBERG
ROD DOWNEY
Affiliation:
SCHOOL OF MATHEMATICS AND STATISTICS VICTORIA UNIVERSITY P.O. BOX 600 WELLINGTON, NEW ZEALAND E-mail: Rod.Downey@vuw.ac.nz
NOAM GREENBERG
Affiliation:
SCHOOL OF MATHEMATICS AND STATISTICS VICTORIA UNIVERSITY P.O. BOX 600 WELLINGTON, NEW ZEALAND E-mail: greenberg@msor.vuw.ac.nz
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Abstract

We introduce a new hierarchy of computably enumerable degrees. This hierarchy is based on computable ordinal notations measuring complexity of approximation of ${\rm{\Delta }}_2^0$ functions. The hierarchy unifies and classifies the combinatorics of a number of diverse constructions in computability theory. It does so along the lines of the high degrees (Martin) and the array noncomputable degrees (Downey, Jockusch, and Stob). The hierarchy also gives a number of natural definability results in the c.e. degrees, including a definable antichain.

Keywords

03D25computably enumerabletotally α-computably approximablemultiple permittinglattice embedding

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Type
Articles
Information
Bulletin of Symbolic Logic , Volume 24 , Issue 1 , March 2018 , pp. 53 - 89
Copyright
Copyright © The Association for Symbolic Logic 2018 

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