  It is known that, for any finite coloring of the naturals, there exists
distinct naturals $e_1,e_2,e_3,e_4$ that are the same color such that
$e_1+e_2=e_3+e_4$. Consider the following statement which we denote S: For
every $\aleph_0$-coloring of the reals there exists distinct reals
$e_1,e_2,e_3,e_4$ such that $e_1+e_2=e_3+e_4$?} Is it true? Erdos showed that S
is equivalent to the negation of the Continuum Hypothesis, and hence S is
indepedent of ZFC. We give an exposition of his proof and some modern
observations about results of this sort.
