A dependent theory with few indiscernibles

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

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