A dependent theory with few indiscernibles

Abstract

We give a full solution to the question of existence of indiscernibles in dependent theories by proving the following theorem: for every $\theta$ there is a dependent theory $T$ of size $\theta$ such that for all $\kappa$ and $\delta$, $\kappa \to {\left(\delta \right)}_{T,1}$ iff $\kappa \to {\left(\delta \right)}_{\theta }^{<\omega }$. This means that unless there are good set theoretical reasons, there are large sets with no indiscernible sequences.

References in corpus (1)

• Stable theories and representation over sets