Аннотации:
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 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 R and provide some new degree spectra of structures.