We continue to talk about L_{omega_1, omega} from last time. This time we introduce Skolem functions and indiscernibles as a way to construct models. We use this to prove an analogue of the Upward Lowenheim-Skolem theorem, just slightly better than the following: If a theory in L_{omega_1, omega} has a model of size Beth_{omega_1}, then it has a model of any infinite size. We will also discuss elementary chains, if time permits.

There will eventually be notes from this series of talks.