Computable Topological Groups

Journal of Symbolic Logic:1-33 (forthcoming)
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We investigate what it means for a (Hausdorff, second-countable) topological group to be computable. We compare several potential definitions based on classical notions in the literature. We relate these notions with the well-established definitions of effective presentability for discrete and profinite groups, and compare our results with similar results in computable topology.



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Computably Compact Metric Spaces.Rodney G. Downey & Alexander G. Melnikov - 2023 - Bulletin of Symbolic Logic 29 (2):170-263.
Hiearchies of Boolean algebras.Lawrence Feiner - 1970 - Journal of Symbolic Logic 35 (3):365-374.
Computable Abelian groups.Alexander G. Melnikov - 2014 - Bulletin of Symbolic Logic 20 (3):315-356,.

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