Journal of Symbolic Logic 75 (3):971-995 (2010)

Abstract
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 nonlow₂ $\Delta _{2}^{0}$ degrees are 0-basis homogeneous bounding. The result of this paper shows that this is an exact characterization of the 0-basis homogeneous bounding $\Delta _{2}^{0}$ degrees
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DOI 10.2178/jsl/1278682211
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References found in this work BETA

Degrees Coded in Jumps of Orderings.Julia F. Knight - 1986 - Journal of Symbolic Logic 51 (4):1034-1042.
Computability of Homogeneous Models.Karen Lange & Robert I. Soare - 2007 - Notre Dame Journal of Formal Logic 48 (1):143-170.
Degree Spectra of Prime Models.Barbara F. Csima - 2004 - Journal of Symbolic Logic 69 (2):430 - 442.
The Degree Spectra of Homogeneous Models.Karen Lange - 2008 - Journal of Symbolic Logic 73 (3):1009-1028.
Prime Models of Computably Enumerable Degree.Rachel Epstein - 2008 - Journal of Symbolic Logic 73 (4):1373-1388.

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Citations of this work BETA

The Degree Spectra of Homogeneous Models.Karen Lange - 2008 - Journal of Symbolic Logic 73 (3):1009-1028.

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