 The structure \(I\) in the previous paragraph involves one fixed object and one fixed class. Since we described the structure today, the class is the class of pigeons in Alfonso’s loft today, not those that will come tomorrow to replace them. If Alfonso Arblaster kills all the pigeons in his loft today, then \(I\) satisfies the quoted sentence today but won’t satisfy it tomorrow, because Alfonso can’t kill the same pigeons twice over. Depending on what you want to use model theory for, you may be happy to evaluate sentences today (the default time), or you may want to record how they are satisfied at one time and not at another. In the latter case you can relativise the notion of model and write ‘\(I \vDash_t S\)’ to mean that \(I\) is a model of \(S\) at time \(t\). The same applies to places, or to anything else that might be picked up by other implicit indexical features in the sentence. For example if you believe in possible worlds, you can index \(\vDash\) by the possible world where the sentence is to be evaluated. Apart from using set theory, model theory is completely agnostic about what kinds of thing exist.