Limitwise monotonic reducibility on sets and on pairs of sets

© 2016, Allerton Press, Inc.We study limitwise monotonic sets and pairs of sets. We investigate the properties of limitwise monotonic reducibility between sets and pairs of sets defined in terms of Σ-reducibility corresponding to initial segment of sets. In addition, we obtain a description of Σ-reducibility of families of a special form in terms of lm-reducibility. At the same time we show the relationship of concepts of lm-reducibility and Σ-reducibility between the pairs of sets