Minimal bounded index subgroup for dependent theories

TL;DR

This paper proves that in dependent theories, the intersection of type definable subgroups with bounded index remains a type definable subgroup with bounded index, highlighting a structural property of such theories.

Contribution

It establishes a new structural result about type definable subgroups in dependent theories, showing stability of bounded index intersections.

Findings

Intersection of type definable subgroups with bounded index is type definable

The result applies to all type definable groups in dependent theories

Provides insight into the structure of definable groups in model theory

Abstract

For a dependent theory T, in C_T for every type definable group G, the intersection of type definable subgroups with bounded index is a type definable subgroup with bounded index.