Separating weak α-change and α-change genericity

Abstract

In [13], a transfinite hierarchy of genericity notions stronger than 1-genericity and weaker than 2-genericity was introduced. We close a line of questioning begun there by showing that for every α⩽ε0 which is a power of ω, there is a Δ20 Turing degree a which is weakly α-change generic, but not α-change generic.