  The theme of the first two sections, is to prepare the framework of how from
a ``complicated'' family of so called index models $I \in K_1$ we build many
and/or complicated structures in a class $K_2$. The index models are
characteristically linear orders, trees with $\kappa+1$ levels (possibly with
linear order on the set of successors of a member) and linearly ordered graphs;
for this we formulate relevant complicatedness properties (called bigness).
  In the third section we show stronger results concerning linear orders. If
for each linear order $I$ of cardinality $\lambda > \aleph_0$ we can attach a
model $M_I \in K_\lambda$ in which the linear order can be embedded such that
for enough cuts of $I$, their being omitted is reflected in $M_I$, then there
are $2^\lambda$ non-isomorphic cases. We also do the work for some
applications.
