I am looking forward to the next part but he has already said something that will be a a problem later on: he said that according to L-S theorem there are countable sets that are models of set theory (ZFC to be precise). This is not really true since it contradicts Goedel's incompleteness theorem. What the method of forcing uses, however, is a pair of theorems by Mostowski: the reflection and the collapse theorem that let one find a model of any finite(ly axiomatizable) portion of ZFC. Finite axiomatizations of set theory (say, GB) have similar tricks. His intuition is right on though.