  A well-ordering principle is a principle of the form: If $X$ is well-ordered
then $F(X)$ is well-ordered, where $F$ is some natural operator transforming
linear orders into linear orders. Many important subsystems of Second-order
Arithmetic of interest in Reverse Mathematics are known to be equivalent to
well-ordering principles.
  We give a unified treatment for proving lower bounds on the logical strength
of various Ramsey-theoretic principles relations using characterizations of the
corresponding formal systems in terms of well-ordering principles.
  Our implications (over $RCA_0$) from combinatorial theorems to $ACA_0$ and
$ACA_0^+$ also establish uniform computable reductions of the corresponding
well-ordering principles to the corresponding Ramsey-type theorems.
