Silver's Theorem

Silver's Theorem, proved by Jack Silver in 1975 and presented that year at the International Congress of Mathematicians, states that if kappa is a singular cardinal of uncountable cofinality and the generalized continuum hypothesis holds for every infinite cardinal below kappa, then it also holds at kappa itself. The result was a surprise, since set theorists had expected forcing to show the generalized continuum hypothesis could fail at such a cardinal even when it held below it, and Silver's proof introduced the master condition technique that became a standard tool in later forcing arguments over large cardinals.