A characterization of the 0-basis homogeneous bounding degrees

Karen Lange
2010 Journal of Symbolic Logic (JSL)  
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
more » ... is homogeneous bounding if any homogenous with a 0-basis has a d -decidable copy. In previous work, we showed that the non low2 Δ2 0 degrees are 0-basis homogeneous bounding. The result of this paper shows that this is an exact characterization of the 0-basis homogeneous bounding Δ2 0 degrees.
doi:10.2178/jsl/1278682211 fatcat:nw6krpdwsfdull2olyp4agacmu