Modules and Infinitary Logics

TL;DR

This paper demonstrates that the theories of abelian groups and R-modules are stable and well-understood even within the context of infinitary logic.

Contribution

It extends the understanding of stability and theory characterization to infinitary logic for abelian groups and R-modules.

Findings

Theories of abelian groups are stable in infinitary logic.

Theories of R-modules are stable in infinitary logic.

Theories are understood to some extent in this logical framework.

Abstract

We prove that the theory of abelian groups and R-modules even in infinitary logic is stable and understood to some extent.