Abstract
Let \(\textbf{K}\) and \(\textbf{M}\) be locally finite quasivarieties of finite type such that \(\textbf{K}\subset \textbf{M}\). If \(\textbf{K}\) is profinite then the filter \([\textbf{K},\textbf{M}]\) in the quasivariety lattice \(\textrm{Lq}(\textbf{M})\) is an atomic lattice and \(\textbf{K}\) has an independent quasi-equational basis relative to \(\textbf{M}\). Applications of these results for lattices, unary algebras, groups, unary algebras, and distributive algebras are presented which concern some well-known problems on standard topological quasivarieties and other problems.
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Acknowledgements
The authors are grateful to the referee for thorough reading the paper and many helpful comments. The second author was supported by the Russian Science Foundation, project no. 22-21-00104.
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Nurakunov, A.M., Schwidefsky, M.V. Profinite Locally Finite Quasivarieties. Stud Logica (2023). https://doi.org/10.1007/s11225-023-10077-y
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DOI: https://doi.org/10.1007/s11225-023-10077-y
Keywords
- Inverse limit
- Locally finite
- Quasi-equational basis
- Quasivariety
- Profinite structure
- Standard quasivariety