Limitwise Monotonic Reducibility of Sets and Σ-Definability of Abelian Groups
D. Kh. Zainetdinov · Russian Mathematics · 2019
The paper is devoted to the study of limitwise monotonic sets, as well as to the investigation of the main structural properties of limitwise monotonic reducibility (for short we will also write lm -reducibility) between sets. In this paper, we obtain a description of the algorithmic dependence between the limitwise monotonic reducibility of sets, which is defined in terms of the Σ-reducibility of the families of initial segments, and the Σ-definability of abelian groups.