  We consider the length of the longest word definable in FO and MSO via a
formula of size n. For both logics we obtain as an upper bound for this number
an exponential tower of height linear in n. We prove this by counting types
with respect to a fixed quantifier rank. As lower bounds we obtain for both FO
and MSO an exponential tower of height in the order of a rational power of n.
We show these lower bounds by giving concrete formulas defining word
representations of levels of the cumulative hierarchy of sets. In addition, we
consider the L\"owenheim-Skolem and Hanf numbers of these logics on words and
obtain similar bounds for these as well.
