I'm not exactly sure if this is what you mean, but the state SQ_{0} that is mentioned on page 15 is the resulting state that you get by combining S_{0} and Q_{0} in the product structure where S_{0} is a state of S_{K1} and Q_{0} is a state of S_{K2}. As it is a new state in a new Kripke (product) structure it simply has a new name, as it is the 0th state in the SQ-product structure (the same holds for SQ_{1} and SQ_{2}).