 The accessibility relation \(R_{\alpha}\) is an equivalence relation connecting \(x\) to all information states \(y\) such that \(y\) is indistinguishable from \(x\), given \(\alpha\)’s hard information at that state \(x\). That is, given what the waiter knows when he is in that state. So, if \(x\) was the waiter’s information state before being informed that you ordered the soda, \(y\) would have included the information that you ordered the espresso, as each option was as good as the other until the waiter was informed otherwise. There is an implicit assumption at work here—that some state \(z\) say, where you ordered both the soda and the espresso, is not in the waiter’s information-range. That is, the waiter knows that \(z\) is not a possibility. Once informed however, the information states supporting your ordering the espresso are eliminated from the range of information corresponding to the waiter’s knowledge. 