The transition semantics presented in Rumberg (J Log Lang Inf 25(1):77–108, 2016a) constitutes a fine-grained framework for modeling the interrelation of modality and time in branching time structures. In that framework, sentences of the transition language L_t are evaluated on transition structures at pairs consisting of a moment and a set of transitions. In this paper, we provide a class of first-order definable Kripke structures that preserves L_t-validity w.r.t. transition structures. As a consequence, for a certain fragment of L_t, validity (...) w.r.t. transition structures turns out to be axiomatizable. The result is then extended to the entire language L_t by means of a quite natural ‘Henkin move’, i.e. by relaxing the notion of validity to bundled structures. (shrink)

Branching time is a popular theory of time that is intended to account for the openness of the future. Generally, branching-time models the openness of the future by positing a multiplicity of concrete alternative futures mirroring all the possible ways the future could unfold. A distinction is drawn in the literature among branching-time theories: those that make use of moment-based structures and those that employ history-based ones. In this paper, I introduce and discuss a particular kind of openness relative to (...) the possibility that time ends (doomsday). I then show that whereas moment-based branching structures cannot represent this kind of openness, history-based structures can account for it. The conclusion is that history-based structures have an advantage over moment-based ones. (shrink)