  We give a number of approximation metatheorems for monotone maximization
problems expressible in the first-order logic, in substantially more general
settings than the previously known. We obtain * constant-factor approximation
algorithm in any class of graphs with bounded expansion, * a QPTAS in any class
with strongly sublinear separators, and * a PTAS in any fractionally
treewidth-fragile class (which includes all common classes with strongly
sublinear separators. Moreover, our tools also give an exact
subexponential-time algorithm in any class with strongly sublinear separators.
