 Note that presentist quantification naturally relates to first-order temporal models with varying domains, while in the semantics based on eternalist quantification the local domains do not play any essential role. In fact, from a technical point of view, eternalist quantification amounts to the assumption that the model has a constant domain, i.e., all local domains equal the global domain. Moreover, in constant domain models the semantics based on presentist quantification coincides with the semantics based on eternalist quantification. Thus, presentist quantification suggests a varying domain semantics, whereas the semantics associated with eternalist quantification is a constant domain semantics, and in what follows we will use these expressions interchangeably.