We study the computational complexity of the FO model checking problem on interval graphs, i.e., intersection graphs of intervals on the real line.The main positive result is that FO model checking and successor-invariant FO model ut solution gel for cats checking can be solved in time O(n log n) for n-vertex interval graphs with representations containing only intervals with lengths from a prescribed finite set.We complement this result by showing that the read more same is not true if the lengths are restricted to any set that is dense in an open subset, e.
g., in the set $(1, 1 + arepsilon)$.