  Our theme is that not every interesting question in set theory is independent
of $ZFC$. We give an example of a first order theory $T$ with countable $D(T)$
which cannot have a universal model at $\aleph_1$ without CH; we prove in $ZFC$
a covering theorem from the hypothesis of the existence of a universal model
for some theory; and we prove --- again in ZFC --- that for a large class of
cardinals there is no universal linear order (e.g. in every
$\aleph_1<\l<2^{\aleph_0}$). In fact, what we show is that if there is a
universal linear order at a regular $\l$ and its existence is not a result of a
trivial cardinal arithmetical reason, then $\l$ ``resembles'' $\aleph_1$ --- a
cardinal for which the consistency of having a universal order is known. As for
singular cardinals, we show that for many singular cardinals, if they are not
strong limits then they have no universal linear order. As a result of the non
existence of a universal linear order, we show the non-existence of universal
models for all theories possessing the strict order property (for example,
ordered fields and groups, Boolean algebras, p-adic rings and fields, partial
orders, models of PA and so on).
