  We analyse the pseudofinite monadic second order theory of words over a fixed
finite alphabet. In particular we present an axiomatisation of this theory,
working in a one-sorted first order framework. The analysis hinges on the fact
that concatenation of words interacts nicely with monadic second order logic.
More precisely, give a signature under which for each natural number k,
equivalence of (monadic second order versions of) words with respect to
formulas of quantifier depth at most k is a congruence for concatenation. We
use our analysis to present an alternative proof of a theorem connecting
recognisable languages and finitely generated free profinite monoids via
extended Stone duality, due to Gehrke, Grigorieff, and Pin.
