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We establish zero-one laws and convergence laws for monadic second-orderlogic (MSO) (and, a fortiori, first-order logic) on a number of interestinggraph classes. In particular, we show that MSO obeys a zero-one law on theclass of connected planar graphs, the class of connected graphs of tree-widthat most $k$ and the class of connected graphs excluding the $k$-clique as aminor. In each of these cases, dropping the connectivity requirement leads to aclass where the zero-one law fails but a convergence law for MSO still holds.

Logical properties of random graphs from small addable classes