Selected methods for the classification of cuts, and their applications

TL;DR

This paper explores four methods for analyzing cuts in ordered algebraic structures, examining their relationships and applications to better understand their properties and significance.

Contribution

It introduces and interrelates four approaches to analyzing cuts in ordered abelian groups and fields, highlighting their applications.

Findings

Analysis of the interconnection between the methods

Identification of applications in ordered algebraic structures

Clarification of properties of ball cuts and invariance groups

Abstract

We consider four approaches to the analysis of cuts in ordered abelian groups and ordered fields, their interconnection, and various applications. The notions we discuss are: ball cuts, invariance group, invariance valuation ring, and cut cofinality.