Definable groups for dependent and 2-dependent theories

Abstract

Let $T$ be a (first order complete) dependent theory, $\mathfrak{C}$ a $\bar{\kappa }$-saturated model of $T$ and $G$ a definable subgroup which is abelian. Among subgroups of bounded index which are the union of $<\bar{\kappa }$ type definable subsets there is a minimal one, i.e. their intersection has bounded index. In fact, the bound is $\le 2^{|T|}$. We then deal with 2-dependent theories, a wider class of first order theories.

Version of 2017

Cited by in corpus (5)

• On n-dependence
• External definability and groups in NIP theories
• On n-dependent groups and fields II
• Dp-finite fields I: infinitesimals and positive characteristic
• Theories without the tree property of the second kind