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A characterization of the 0-basis homogeneous bounding degrees

Published online by Cambridge University Press:  12 March 2014

Karen Lange
Karen Lange*
Affiliation:
Mathematics Department, University of Notre Dame, 255 Hurley Hall, Notre Dame, In 46556-4618, USA. E-mail: klangel@nd.edu
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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 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 3 , September 2010 , pp. 971 - 995
Copyright
Copyright © Association for Symbolic Logic 2010

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