A characterization of the 0-basis homogeneous bounding degrees

We say a countable model A has a 0-basis if the types realized in A are uniformly computable. We say A has a (d-)decidable copy if there exists a model B = A such that the elementary diagram of B is (d-)computable. Goncharov, Millar, and Peretyat'kin independently showed there exists a homogeneous model A 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 A with a 0-basis but no d-decidable copy. A degree d is 0-basis homogeneous bounding if any homogenous A with a 0-basis has a d-decidable copy. In previous work we showed that the nonlow2 0 2 degrees are 0-basis homogeneous bounding. The result of this paper shows that this is an exact characterization of the 0-basis homogeneous bounding 0 2 degrees.

• Type: Journal
• Year: 2010
• Where: JSYML
• Authors: Karen Lange
• Keywords: 0-basis Homogeneous Bounding, Decidable Copy, JSYML 2010, Model