8 found
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  1. Asher M. Kach, Karen Lange & Reed Solomon (2013). Degrees of Orders on Torsion-Free Abelian Groups. Annals of Pure and Applied Logic 164 (7-8):822-836.
    We show that if H is an effectively completely decomposable computable torsion-free abelian group, then there is a computable copy G of H such that G has computable orders but not orders of every degree.
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  2.  10
    Karen Lange (2008). The Degree Spectra of Homogeneous Models. Journal of Symbolic Logic 73 (3):1009-1028.
    Much previous study has been done on the degree spectra of prime models of a complete atomic decidable theory. Here we study the analogous questions for homogeneous models. We say a countable model A has a d-basis if the types realized in A are all computable and the Turing degree d can list $\Delta _{0}^{0}$ -indices for all types realized in A. We say A has a d-decidable copy if there exists a model B ≅ A such that the elementary (...)
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  3.  14
    Paola D'Aquino, Julia Knight & Karen Lange (2011). Limit Computable Integer Parts. Archive for Mathematical Logic 50 (7-8):681-695.
    Let R be a real closed field. An integer part I for R is a discretely ordered subring such that for every ${r \in R}$ , there exists an ${i \in I}$ so that i ≤ r < i + 1. Mourgues and Ressayre (J Symb Logic 58:641–647, 1993) showed that every real closed field has an integer part. The procedure of Mourgues and Ressayre appears to be quite complicated. We would like to know whether there is a simple procedure, (...)
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  4.  7
    Karen Lange & Robert I. Soare (2007). Computability of Homogeneous Models. Notre Dame Journal of Formal Logic 48 (1):143-170.
    In the last five years there have been a number of results about the computable content of the prime, saturated, or homogeneous models of a complete decidable theory T in the spirit of Vaught's "Denumerable models of complete theories" combined with computability methods for degrees d ≤ 0′. First we recast older results by Goncharov, Peretyat'kin, and Millar in a more modern framework which we then apply. Then we survey recent results by Lange, "The degree spectra of homogeneous models," which (...)
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  5.  4
    Karen Lange (2010). A Characterization of the 0 -Basis Homogeneous Bounding Degrees. Journal of Symbolic Logic 75 (3):971-995.
    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 (...)
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  6.  2
    Alf Dolich, Julia F. Knight, Karen Lange & David Marker (2015). Representing Scott Sets in Algebraic Settings. Archive for Mathematical Logic 54 (5-6):631-637.
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  7.  2
    Paola D’Aquino, Julia Knight & Karen Lange (2015). Erratum To: Limit Computable Integer Parts. Archive for Mathematical Logic 54 (3-4):487-489.
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  8. Peter A. Cholak, Peter M. Gerdes & Karen Lange (2012). On N-Tardy Sets. Annals of Pure and Applied Logic 163 (9):1252-1270.