Jack Silver
Jack Silver | |
|---|---|
 Jack Silver in 1986 (photo by George Bergman) | |
| Born | Jack Howard Silver April 23, 1942 |
| Died | December 22, 2016 (aged 74) |
| Nationality | American |
| Alma mater | University of California, Berkeley |
| Known for | Silver forcing |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of California, Berkeley |
| Thesis | Some Applications of Model Theory in Set Theory (1966) |
| Doctoral advisor | Robert Lawson Vaught |
| Doctoral students | Jeremy Avigad John P. Burgess Randall Dougherty Martin Goldstern Concha Gómez Richard Zach |
Jack Howard Silver (23 April 1942 – 22 December 2016logician at the University of California, Berkeley.
Born in Montana, he earned his
Alfred P. Sloan Research Fellowship from 1970 to 1972. Silver made several contributions to set theory in the areas of large cardinals and the constructible universe
L.
Contributions
In his 1975 paper "On the Singular Cardinals Problem", Silver
ZFC. He introduced the notion of a master condition, which became an important tool in forcing proofs involving large cardinals.[3]
Silver proved the consistency of
Silver indiscernibles and generalizing the notion of a Kurepa tree (called Silver's Principle). 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. Drake.[4]
Silver's original work involving large cardinals was perhaps motivated by the goal of showing the inconsistency of an uncountable measurable cardinal; instead he was led to discover indiscernibles in L assuming a measurable cardinal exists.
Selected publications
- Silver, Jack H. (1971). "Some applications of model theory in set theory". Annals of Mathematical Logic 3(1), pp. 45–110.
- Silver, Jack H. (1973). "The bearing of large cardinals on constructibility". In Studies in Model Theory, MAA Studies in Mathematics 8, pp. 158–182.
- Silver, Jack H. (1974). "Indecomposable ultrafilters and 0#". In Proceedings of the Tarski Symposium, Proceedings of Symposia in Pure Mathematics XXV, pp. 357–363.
- Silver, Jack (1975). "On the singular cardinals problem". In Proceedings of the International Congress of Mathematicians 1, pp. 265–268.
- Silver, Jack H. (1980). "Counting the number of equivalence classes of Borel and coanalytic equivalence relations". Annals of Mathematical Logic 18(1), pp. 1–28.
References
- ^ Group in Logic and the Methodology of Science, "Jack Howard Silver", University of California–Berkeley
- ^ Jack Silver at the Mathematics Genealogy Project
- ^ Cummings, James (2009). "Iterated Forcing and Elementary Embeddings". In Handbook of Set Theory, Springer, pp. 775–883, esp. pp. 814ff.
- ISBN 0-444-10535-2
External links
- Jack Silver at Berkeley
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| Academics | |
