The Weak Reflection Principle for omega_2 is the statement that
for every stationary subset S of P_{omega_1}(omega_2), there is
an uncountable ordinal alpha in omega_2 such that
S cap P_{omega_1}(alpha) is stationary in P_{omega_1}(alpha).

The Reflection Principle for omega_2 is the statement that
for every stationary subset S of P_{omega_1}(omega_2),
there is an ordinal alpha in omega_2 with cofinality omega_1
such that S cap P_{omega_1}(alpha) is stationary in P_{omega_1}(alpha).

A long outstanding problem in set theory has been the question whether the
Weak Reflection Principle for omega_2 implies the Reflection Principle for
omega_2. In this talk I will discuss my recent solution to this problem.