Jack Silver

Jack Howard Silver (born April 23, 1942 in Missoula , Montana , † December 22, 2016 ) was an American mathematician who dealt with set theory.

Jack Silver 1986

Silver received his PhD in 1966 from the University of California, Berkeley with Robert Vaught (Some applications of model theory in set theory). He was a professor at the University of California, Berkeley, where he was most recently Professor Emeritus.

Silver made significant advances in the problem of singular cardinal numbers . He solved the problem for cardinal numbers with a terminality greater than . In particular, he proved that from the axioms of ZFC it follows: If the generalized continuum hypothesis holds for every cardinal number less than , a singular cardinal number with uncountable affinity (greater than ), then it also holds for itself ( Silver's theorem ). That is, for all infinite cardinal numbers , then applies . The sentence was surprising at the time, because almost all set theorists were convinced that the opposite would be consistent with ZFC (including Silver himself, as he stated in his lecture at the ICM in Vancouver). ${\ displaystyle \ aleph _ {0}}$ ${\ displaystyle \ aleph _ {\ alpha}}$ ${\ displaystyle \ aleph _ {0}}$ ${\ displaystyle \ aleph _ {\ alpha}}$ ${\ displaystyle 2 ^ {\ aleph _ {\ beta}} = \ aleph _ {\ beta +1}}$ ${\ displaystyle \ aleph _ {\ beta} <\ aleph _ {\ alpha}}$ ${\ displaystyle 2 ^ {\ aleph _ {\ alpha}} = \ aleph _ {\ alpha +1}}$

In 1970 he received a research grant from the Alfred P. Sloan Foundation ( Sloan Research Fellowship ). In 1974 he was invited speaker at the International Congress of Mathematicians (ICM) in Vancouver (On the singular cardinals problem).

His PhD students include William Mitchell , Karel Prikry, and Randall Dougherty .

Web links

Individual evidence

↑ richardzach.org , accessed March 22, 2017
↑ Ann. Math. Logic, Vol. 3, 1971, pp. 45-110. Among other things, ("Zero Sharp") is introduced in the work. ${\ displaystyle 0 ^ {\ #}}$
^ Lecture at the International Congress of Mathematicians 1974
↑ that is, the confinality of is less than ${\ displaystyle \ aleph _ {\ alpha}}$ ${\ displaystyle \ aleph _ {\ alpha}}$
^ Mathematics Genealogy Project

personal data
SURNAME	Silver, Jack
ALTERNATIVE NAMES	Silver, Jack Howard (full name)
BRIEF DESCRIPTION	American mathematician
DATE OF BIRTH	April 23, 1942
PLACE OF BIRTH	Missoula , Montana
DATE OF DEATH	December 22, 2016

[1] richardzach.org , accessed March 22, 2017

[2] Ann. Math. Logic, Vol. 3, 1971, pp. 45-110. Among other things, ("Zero Sharp") is introduced in the work. ${\ displaystyle 0 ^ {\ #}}$

[3] Lecture at the International Congress of Mathematicians 1974

[4] that is, the confinality of is less than ${\ displaystyle \ aleph _ {\ alpha}}$ ${\ displaystyle \ aleph _ {\ alpha}}$

[5] Mathematics Genealogy Project