  There are familiar examples of computable structures having various
computable Scott ranks. There are also familiar structures, such as the
Harrison ordering, which have Scott rank $\omega_1^{CK}+1$. Makkai produced a
structure of Scott rank $\omega_1^{CK}$, which can be made computable, and
simplified so that it is just a tree. In the present paper, we show that there
are further computable structures of Scott rank $\omega_1^{CK}$ in the
following classes: undirected graphs, fields of any characteristic, and linear
orderings. The new examples share with the Harrison ordering, and the tree just
mentioned, a strong approximability property.
