Albert Visser: Sharing Time Across Branches

Branching time is a popular model in the modal study of time. A branching time structure, however, is simply an ordering with certain extra properties. Such structures are intrinsically too poor to capture the idea of simulaneity among moments across branches. However, we do want to be able to analyse sentences like, "If I had started to prepare this talk earlier, I would not have to hurry now"'. So some extra structure is needed. We consider the minimal idea of adding a *chrono-function* to a branching time structure that maps moments to times on a linear time axis. In the talk we provide a descriptive framework for branching time structures with chrono-function. We will formulate some conditions under which branching time structures can be extended with a chrono-function satisfying various further desirable properties. We will discuss some suprising examples that show that some natural branching time structures only  have chrono-functions that lack some salient good properties. Specifically, these natural models will have histories that do not reach certain moments on the time axis. So, in these models, we could have been out of time now, in the literal sense that there could have been no time now.