Abstract
We establish that the isomorphism problem for the classes of computable nilpotent rings, distributive lattices, nilpotent groups, and nilpotent semigroups is \(\Sigma _{1}^{1}\)-complete, which is as complicated as possible. The method we use is based on uniform effective interpretations of computable binary relations into computable structures from the corresponding algebraic classes.
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The authors thank the anonymous referee for numerous helpful suggestions that greatly improved this paper. The first four authors are grateful for support from NSF Grant DMS-1600025. The first author was partially supported by Simons Foundation Collaboration Grant 429466 and GW Dean’s Research Chair award. The second author was partially supported by AMS-Simons Foundation Collaboration Grant 626304.
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Harizanov, V.S., Lempp, S., McCoy, C.F.D. et al. On the isomorphism problem for some classes of computable algebraic structures. Arch. Math. Logic 61, 813–825 (2022). https://doi.org/10.1007/s00153-021-00811-5
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DOI: https://doi.org/10.1007/s00153-021-00811-5
Keywords
- Isomorphism problem
- Computable structure
- Nilpotent structure
- Distributive lattice
- Effective transformation