The Monadic Theory of Tree-like Structures

Initiated by the work of Buchi, Lauchli, Rabin, and Shelah in the late 60s, the investigation of monadic second-order logic (MSO) has received continuous attention. The attractiveness of MSO is due to the fact that, on the one hand, it is quite expressive subsuming - besides first-order logic - most modal logics, in particular the μ-calculus. On the other hand, MSO is simple enough such that model-checking is still decidable for many structures. Hence, one can obtain decidability results for several logics by just considering MSO.