Open AccessHierarchy of Computably Enumerable Degrees II
Author(s) -
Rodney G. Downey,
Noam Greenberg,
Ellen Hammatt
Publication year - 2021
Publication title -
new zealand journal of mathematics
Language(s) - English
Resource type - Journals
eISSN - 1179-4984
pISSN - 1171-6096
DOI - 10.53733/133
Subject(s) - transfinite number , hierarchy , mathematics , computability , analytical hierarchy , turing , discrete mathematics , pure mathematics , computer science , mathematical economics , analytic hierarchy process , economics , market economy , programming language
A transfinite hierarchy of Turing degrees of c.e.\ sets has been used to calibrate the dynamics of families of constructions in computability theory, and yields natural definability results. We review the main results of the area, and discuss splittings of c.e.\ degrees, and finding maximal degrees in upper cones.