Indiscernible sequence over a model

Question

I'm trying to prove the following proposition. Any hint would be appreciated.

Proposition. Let $T$ be a theory and let $(b_i)_{i<\omega}$ be an indiscernible sequence over a set of parameters $A$. Then there is a model $\mathcal{M}$ of $T$ such that:

(i) $A\subset \mathcal{M}$

(ii) $(b_i)_{i<\omega}$ is an indiscernible sequence over $\mathcal{M}$.

Answer 1

1. Let $M'$ be any model containing $A$.
2. Find a new sequence $(b_i')$ which is based on $(b_i)$ and indiscernible over $M'$.
3. Find an automorphism $\sigma$ of the monster model which fixes $A$ and moves $(b_i')$ to $(b_i)$.
4. Let $M=\sigma(M')$.