  We introduce the definability strength of combinatorial principles. In terms
of definability strength, a combinatorial principle is strong if solving a
corresponding combinatorial problem could help in simplifying the definition of
a definable set. We prove that some consequences of Ramsey's Theorem for
colorings of pairs could help in simplifying the definitions of some
$\Delta^0_2$ sets, while some others could not. We also investigate some
consequences of Ramsey's Theorem for colorings of longer tuples. These results
of definability strength have some interesting consequences in reverse
mathematics, including strengthening of known theorems in a more uniform way
and also new theorems.
