Abstract
The current work studies the limitwise monotonic spectra introduced by Downey, Kach and Turetsky [6]. In the first part of the paper, we study the limitwise monotonic spectra of subsets and sequences of subsets of \(\mathbb N\). In particular, we study their measure-theoretical and topological properties. Then we generalize them to the spectra of subsets and sequences of subsets of \(\mathbb R\) and provide some new degree spectra of structures.
The work is supported by the Russian Science Foundation (grant no. 18-11-00028) and performed under the development program of Volga Region Mathematical Center (agreement no. 075-02-2020-1478).
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I am very grateful to the referees for the careful reading of the paper and for their comments and detailed suggestions, which helped me to improve the manuscript considerably.
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Faizrahmanov, M. (2021). Limitwise Monotonic Spectra and Their Generalizations. In: De Mol, L., Weiermann, A., Manea, F., Fernández-Duque, D. (eds) Connecting with Computability. CiE 2021. Lecture Notes in Computer Science(), vol 12813. Springer, Cham. https://doi.org/10.1007/978-3-030-80049-9_17
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