  What are the most general principles in set theory relating forceability and
truth? As with Solovay's celebrated analysis of provability, both this question
and its answer are naturally formulated with modal logic. We aim to do for
forceability what Solovay did for provability. A set theoretical assertion psi
is forceable or possible, if psi holds in some forcing extension, and
necessary, if psi holds in all forcing extensions. In this forcing
interpretation of modal logic, we establish that if ZFC is consistent, then the
ZFC-provable principles of forcing are exactly those in the modal theory known
as S4.2.
