In [Cantor's Attic][1] it is stated that an $\omega$-Erdös cardinal is a stationary limit of ineffable cardinals, and Jech book is given as a reference, but I cannot find this result in that book. I have seen proofs in other sources using that Erdös cardinals are subtle, but since Jech does not define subtle cardinals, I wonder whether there is a more direct proof.

Jech proves (Theorem 17.33) that there is an ineffable cardinal below $\eta_\omega$ by constructing an elementary submodel of $V_{\eta_\omega}$ with a set of indiscernibles and a non-trivial elementary embedding. Then the critical point in ineffable. By adding a set of constants to the formal language I can ensure that the critical point is large, so I obtain an unbounded set of ineffable cardinals below $\eta_\omega$ (and the proof works for any $\eta_\alpha$), but how can I ensure a stationary set of ineffable cardinals?


  [1]: http://cantorsattic.info/Erdos