A Short Note on Infinite Union/Intersection of Omega Regular Languages
  We in this paper show that omega regular languages are not closed under infinite union and intersection. As an attempt, we propose to add step variables and quantifiers to temporal logics to enhance the expressiveness of the underlying logic. We also show that doing this would cause undecidability in satisfiability, even if for a rather limited fragment of temporal logic. 
Wanwei Liu
cs.FL cs.LO