In this paper we explore the connections between the
monadic second-order theory of one successor MSO[<] for
short) and the theories of omega-layered structures for time
granularity. We first prove that the decision problem for
MSO[<] and that for a suitable first-order theory of the upward
unbounded layered structure are inter-reducible. Then, we show that a similar result holds for suitable chain variants of the MSO theory of the totally unbounded layered structure (this allows us to solve a decision problem about theories of time granularity left open by Franceschet et al. [FRA 06])).
