1 results
A HIERARCHY OF COMPUTABLY ENUMERABLE DEGREES
-
- Journal:
- Bulletin of Symbolic Logic / Volume 24 / Issue 1 / March 2018
- Published online by Cambridge University Press:
- 26 April 2018, pp. 53-89
- Print publication:
- March 2018
-
- Article
- Export citation
-
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.
