  Baker's technique is a powerful tool for designing polynomial-time
approximation schemes, in particular for all optimization problems expressible
in monotone first-order logic. However, it can only be used in rather
restricted graph classes. We show that maximization problems expressible in
monotone first-order logic admit PTAS under a much weaker assumption of
fractional treewidth-fragility, and QPTAS on all hereditary classes with
sublinear separators.
