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  1.  13
    Continuous Logic and Borel Equivalence Relations.Andreas Hallbäck, Maciej Malicki & Todor Tsankov - 2023 - Journal of Symbolic Logic 88 (4):1725-1752.
    We study the complexity of isomorphism of classes of metric structures using methods from infinitary continuous logic. For Borel classes of locally compact structures, we prove that if the equivalence relation of isomorphism is potentially $\mathbf {\Sigma }^0_2$, then it is essentially countable. We also provide an equivalent model-theoretic condition that is easy to check in practice. This theorem is a common generalization of a result of Hjorth about pseudo-connected metric spaces and a result of Hjorth–Kechris about discrete structures. As (...)
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  2.  33
    The additive group of the rationals does not have an automatic presentation.Todor Tsankov - 2011 - Journal of Symbolic Logic 76 (4):1341-1351.
    We prove that the additive group of the rationals does not have an automatic presentation. The proof also applies to certain other abelian groups, for example, torsion-free groups that are p-divisible for infinitely many primes p, or groups of the form ⊕ p∈I Z(p ∞ ), where I is an infinite set of primes.
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  3.  14
    Decidability of Definability.Manuel Bodirsky, Michael Pinsker & Todor Tsankov - 2013 - Journal of Symbolic Logic 78 (4):1036-1054.
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