Jack Howard Silver (23 April 1942 – 22 December 2016[1]) was a set theorist and logician at the University of California, Berkeley.

Born in Montana, he earned his Ph.D. in Mathematics at Berkeley in 1966 under Robert Vaught[2] before taking a position at the same institution the following year.

Prior to Silver's proof, many mathematicians believed that a forcing argument would yield that the negation of the theorem is consistent with ZFC.

With the introduction of the so-called Silver machines he was able to give a fine structure free proof of Jensen's covering lemma.

He discovered 0# ("zero sharp") in his 1966 Ph.D. thesis, discussed in the graduate textbook Set Theory: An Introduction to Large Cardinals by Frank R.