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  1.  14
    Tame Expansions of $\omega$ -Stable Theories and Definable Groups.Haydar Göral - 2019 - Notre Dame Journal of Formal Logic 60 (2):161-194.
    We study groups definable in tame expansions of ω-stable theories. Assuming several tameness conditions, we obtain structural theorems for groups definable and interpretable in these expansions. As our main example, by characterizing independence in the pair, where K is an algebraically closed field and G is a multiplicative subgroup of K× with the Mann property, we show that the pair satisfies the assumptions. In particular, this provides a characterization of definable and interpretable groups in in terms of algebraic groups in (...)
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  2.  17
    Algebraic numbers with elements of small height.Haydar Göral - 2019 - Mathematical Logic Quarterly 65 (1):14-22.
    In this paper, we study the field of algebraic numbers with a set of elements of small height treated as a predicate. We prove that such structures are not simple and have the independence property. A real algebraic integer is called a Salem number if α and are Galois conjugate and all other Galois conjugates of α lie on the unit circle. It is not known whether 1 is a limit point of Salem numbers. We relate the simplicity of a (...)
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  3.  25
    Interpretable groups in Mann pairs.Haydar Göral - 2018 - Archive for Mathematical Logic 57 (3-4):203-237.
    In this paper, we study an algebraically closed field \ expanded by two unary predicates denoting an algebraically closed proper subfield k and a multiplicative subgroup \. This will be a proper expansion of algebraically closed field with a group satisfying the Mann property, and also pairs of algebraically closed fields. We first characterize the independence in the triple \\). This enables us to characterize the interpretable groups when \ is divisible. Every interpretable group H in \\) is, up to (...)
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