  Let I be a dense linear order with a left endpoint but no right endpoint. We
consider the lattice L(I) of finite unions of closed intervals of I. This
lattice arises naturally in the setting of o-minimality, as these are precisely
the closed definable sets in any o-minimal expansion of I. Our main result says
that L(I), the expansion of the lattice by constants for the empty set and the
smallest element of I (viewed as a singleton subset) as well as four unary
functions, is model-complete. The proof of the main result makes use of
previous results regarding the weak monadic second order theory of I from the
authors PhD thesis.
