I'm not exactly sure if this is what you mean, but the state SQ0 that is mentioned on page 15 is the resulting state that you get by combining S0 and Q0 in the product structure where S0 is a state of SK1 and Q0 is a state of SK2. 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 SQ1 and SQ2).