Arrow's impossibility theorem was set out in his PhD thesis, Social choice and individual values. It shows the impossibility of designing rules for social decision making that obey all of a number of 'reasonable' criteria. It is often known as Arrow's paradox.
General equilibrium theory
Working with Gerard Debreu (who won the Nobel prize for this work in 1983), Arrow produced the first rigorous proof of the existence of a market clearing equilibrium, given certain restrictive assumptions. See general equilibrium.
