A STRUCTURAL DICHOTOMY IN THE ENUMERATION DEGREES
Hristo Ganchev, ISKANDER SH. KALIMULLIN, Joseph S. Miller, Mariya I. Soskova · Journal of Symbolic Logic · 2020
Abstract We give several new characterizations of the continuous enumeration degrees. The main one proves that an enumeration degree is continuous if and only if it is not half of a nontrivial relativized $\mathcal {K}$ -pair. This leads to a structural dichotomy in the enumeration degrees.