Computably enumerable equivalence relations (ceers) received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility ⩽c. This gives rise to a rich degree structure. In this paper, we lift the study of c-degrees to the Δ02 case. In doing so, we rely on the Ershov hierarchy. For any notation a for a non-zero computable ordinal, we prove several algebraic properties of the degree structure induced by ⩽c on the Σ−1a∖Π−1a equivalence relations. A special focus of our work is on the (non)existence of infima and suprema of c-degrees.
Bazhenov, N., Mustafa, M., San Mauro, L., Sorbi, A., & Yamaleev, M. (2020). Classifying equivalence relations in the Ershov hierarchy. Archive for Mathematical Logic, 1-30. . https://doi.org/10.1007/s00153-020-00710-1