Translator Disclaimer
September 2010 A characterization of the 0-basis homogeneous bounding degrees
Karen Lange
J. Symbolic Logic 75(3): 971-995 (September 2010). DOI: 10.2178/jsl/1278682211

Abstract

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 d0' 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 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.

Citation

Download Citation

Karen Lange. "A characterization of the 0-basis homogeneous bounding degrees." J. Symbolic Logic 75 (3) 971 - 995, September 2010. https://doi.org/10.2178/jsl/1278682211

Information

Published: September 2010
First available in Project Euclid: 9 July 2010

zbMATH: 1213.03045
MathSciNet: MR2723778
Digital Object Identifier: 10.2178/jsl/1278682211

Rights: Copyright © 2010 Association for Symbolic Logic

JOURNAL ARTICLE
25 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.75 • No. 3 • September 2010
Back to Top