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8Uri Andrews. A new spectrum of recursive models using an amalgamation construction. The Journal of Symbolic Logic, vol. 73 (2011), no. 3, pp. 883–896. - Bakhadyr Khoussainov and Antonio Montalbán. A computable ℵ 0 -categorical structure whose theory computes true arithmetic. The Journal of Symbolic Logic, vol. 72 (2010), no. 2, pp. 728–740 (review)Bulletin of Symbolic Logic 19 (3): 400-401. 2013.
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26Torsion-free abelian groups with optimal Scott familiesJournal of Mathematical Logic 18 (1): 1850002. 2018.We prove that for any computable successor ordinal of the form α = δ + 2k there exists computable torsion-free abelian group that is relatively Δα0 -categorical and not Δα−10 -categorical. Equivalently, for any such α there exists a computable TFAG whose initial segments are uniformly described by Σαc infinitary computable formulae up to automorphism, and there is no syntactically simpler family of formulae that would capture these orbits. As far as we know, the problem of finding such optimal e…Read more
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12New Degree Spectra of Abelian GroupsNotre Dame Journal of Formal Logic 58 (4): 507-525. 2017.We show that for every computable ordinal of the form β=δ+2n+1>1, where δ is zero or a limit ordinal and n∈ω, there exists a torsion-free abelian group having an X-computable copy if and only if X is nonlowβ.
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16Computable Abelian groupsBulletin of Symbolic Logic 20 (3). 2014.We provide an introduction to methods and recent results on infinitely generated abelian groups with decidable word problem
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61Classes of Ulm type and coding rank-homogeneous trees in other structuresJournal of Symbolic Logic 76 (3). 2011.The first main result isolates some conditions which fail for the class of graphs and hold for the class of Abelian p-groups, the class of Abelian torsion groups, and the special class of "rank-homogeneous" trees. We consider these conditions as a possible definition of what it means for a class of structures to have "Ulm type". The result says that there can be no Turing computable embedding of a class not of Ulm type into one of Ulm type. We apply this result to show that there is no Turing co…Read more
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20On Δ 2 0 -categoricity of equivalence relationsAnnals of Pure and Applied Logic 166 (9): 851-880. 2015.
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68Decidability and Computability of Certain Torsion-Free Abelian GroupsNotre Dame Journal of Formal Logic 51 (1): 85-96. 2010.We study completely decomposable torsion-free abelian groups of the form $\mathcal{G}_S := \oplus_{n \in S} \mathbb{Q}_{p_n}$ for sets $S \subseteq \omega$. We show that $\mathcal{G}_S$has a decidable copy if and only if S is $\Sigma^0_2$and has a computable copy if and only if S is $\Sigma^0_3$
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23Abelian p-groups and the Halting problemAnnals of Pure and Applied Logic 167 (11): 1123-1138. 2016.
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National Research University Higher School of EconomicsUndergraduate
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Freedom and Liberty |
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Toleration in Normative Theories |
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