Weak MSO+U with Path Quantifiers over Infinite Trees
arXiv:1404.7278
Abstract
This paper shows that over infinite trees, satisfiability is decidable for weak monadic second-order logic extended by the unbounding quantifier U and quantification over infinite paths. The proof is by reduction to emptiness for a certain automaton model, while emptiness for the automaton model is decided using profinite trees.
version of an ICALP 2014 paper with appendices