  It is consistent that there is a partial order (P,<) of size aleph_1 such
that every monotone (unary) function from P to P is first order definable in
(P,<).
  The partial order is constructed in an extension obtained by finite support
iteration of Cohen forcing.
  The main points is that (1) all monotone functions from P to P will
(essentially) have countable range (this uses a Delta-system argument) and (2)
that all countable subsets of P will be first order definable, so we have to
code these countable sets into the partial order. Amalgamation of finite
structures plays an essential role.
