Limitwise Monotonic Reducibility of Sets and Σ-Definability of Abelian Groups
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.
Key wordslimitwise monotonic function limitwise monotonic set limitwise monotonic reducibility family of subsets of natural numbers Σ-reducibility Σ-definability abelian group hereditarily finite superstructure
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The work was done at the expense of subsidies allocated to the Kazan Federal University for the implementation of the state assignment in the field of scientific activity (project No. 1.1515.2017/4.6).
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