Published online by Cambridge University Press: 12 March 2014
We say a countable model has a 0-basis if the types realized in
are uniformly computable. We say
has a (d-)decidable copy if there exists a model
≅
such that the elementary diagram of
is (d-)computable. Goncharov, Millar, and Peretyat'kin independently showed there exists a homogeneous model
with a 0-basis but no decidable copy. We extend this result here. Let d ≤ 0′ be any low2 degree. We show that there exists a homogeneous model
with a 0-basis but no d-decidable copy. A degree d is 0-basis homogeneous bounding if any homogenous
with a 0-basis has a d-decidable copy. In previous work, we showed that the non low2 Δ20 degrees are 0-basis homogeneous bounding. The result of this paper shows that this is an exact characterization of the 0-basis homogeneous bounding Δ20 degrees.