Jack Silver

Jack Howard Silver (23 April 1942 to 22 December 2016) was an American set theorist and logician at the University of California, Berkeley. Born in Montana, he took his doctorate at Berkeley in 1966 under Robert Vaught and joined the faculty there the following year. His contributions to set theory lie in large cardinals and the constructible universe L. In his 1966 thesis he discovered zero sharp, and he introduced the notion of a master condition, an important tool in forcing arguments about large cardinals. In a 1975 paper on the singular cardinals problem he proved that if a singular cardinal of uncountable cofinality has the generalized continuum hypothesis holding below it, then it holds at the cardinal itself, a result that surprised those who expected forcing to make its negation consistent. He also proved the consistency of Chang conjecture and is credited with Silver indiscernibles and Silver machines.