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| [[File:Kenneth Kunen.jpg|thumb|220px|Kenneth Kunen]]
| | Friends call him Royal. Arizona has usually been my living place but my spouse desires us to transfer. Bookkeeping has been his day occupation for a while. Playing crochet is something that I've done for years.<br><br>Take a look at my homepage: extended car warranty ([http://www.strawberrystudio.co.uk/UserProfile/tabid/43/userId/64649/Default.aspx please click the next site]) |
| '''Herbert Kenneth Kunen''' (born August 2, 1943) is an emeritus professor of [[mathematics]] at the [[University of Wisconsin–Madison]]<ref>http://www.math.wisc.edu/~apache/emeriti.html</ref> who works in [[set theory]] and its applications to various areas of mathematics, such as set-theoretic [[topology]] and [[measure theory]]. He also works on [[associativity|non-associative]] algebraic systems, such as [[quasigroup|loops]], and uses computer software, such as the [[Otter theorem prover]], to derive theorems in these areas.
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| Kunen showed that if there exists a nontrivial elementary embedding ''j'':''L''→''L'' of the [[constructible universe]], then [[zero sharp|0<sup>#</sup>]] exists.
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| He proved the consistency of a normal, <math>\aleph_2</math>-saturated ideal on <math>\aleph_1</math> from the consistency of the existence of a [[huge cardinal]]. He introduced the method of iterated [[ultrapower]]s, with which he proved that if <math>\kappa</math> is a [[measurable cardinal]] with <math>2^\kappa>\kappa^+</math> or <math>\kappa</math> is a [[strongly compact cardinal]] then there is an [[inner model]] of set theory with <math>\kappa</math> many measurable cardinals. He proved [[Kunen's inconsistency theorem]] showing the impossibility of a nontrivial elementary embedding <math>V\to V</math>, which had been suggested as a [[large cardinal]] assumption (a [[Reinhardt cardinal]]).
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| Away from the area of large cardinals, Kunen is known for intricate forcing and combinatorial constructions. He proved that it is consistent that the Martin Axiom first fails at a singular cardinal and constructed
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| under CH a compact L-space supporting a nonseparable measure. He also showed that <math>P(\omega)/Fin</math> has no increasing chain of length <math>\omega_2 </math> in the standard Cohen model
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| where the continuum is <math>\aleph_2</math>.
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| Kunen received his [[Ph.D.]] in 1968 from [[Stanford University]],<ref>{{MathGenealogy|id=9055}}</ref> where he was supervised by [[Dana Scott]].
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| ==Selected publications==
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| * ''The Foundations of Mathematics''. College Publications, 2009. ISBN 978-1-904987-14-7.
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| * ''[[Set Theory: An Introduction to Independence Proofs]]''. North-Holland, 1980. ISBN 0-444-85401-0.<ref>{{cite journal|author=Henson, C. Ward|title=Review: ''Set theory, an introduction to independence proofs'', by Kenneth Kunen|journal=Bull. Amer. Math. Soc. (N.S.)|year=1984|volume=10|issue=1|pages=129–131|url=http://www.ams.org/journals/bull/1984-10-01/S0273-0979-1984-15214-5/S0273-0979-1984-15214-5.pdf}}</ref>
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| * (co-edited with Jerry E. Vaughan). ''Handbook of Set-Theoretic Topology''. North-Holland, 1984. ISBN 0-444-86580-2.
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| ==Bibliography==
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| The journal [[Topology and its Applications]] has dedicated a special issue to "Ken" Kunen,<ref>{{cite journal|editor=Hart, Joan|title=Special Issue: Ken Kunen|date=1 Dec 2011|journal=Topology and Its Applications|volume=158|issue=18|pages=2443–2564|url=http://www.sciencedirect.com/science/journal/01668641/158/18}}</ref> containing a biography by [[Arnold W. Miller]], and surveys about Kunen research in various fields by [[Mary Ellen Rudin]], [[Akihiro Kanamori]], [[István Juhász (mathematician)|István Juhász]], [[Jan van Mill]], [[Dikran Dikranjan]], and [[Michael Kinyon]].
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| ==References==
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| <references/>
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| ==External links==
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| *[http://www.math.wisc.edu/~kunen/ Kunen's home page]
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| {{Authority control|VIAF=66528170}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Kunen, Kenneth
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = American mathematician
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| | DATE OF BIRTH = August 2, 1943
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| | PLACE OF BIRTH =
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| | DATE OF DEATH =
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| | PLACE OF DEATH =
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| }}
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| {{DEFAULTSORT:Kunen, Kenneth}}
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| [[Category:1943 births]]
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| [[Category:Living people]]
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| [[Category:American mathematicians]]
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| [[Category:20th-century mathematicians]]
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| [[Category:21st-century mathematicians]]
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| [[Category:Set theorists]]
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| [[Category:Stanford University alumni]]
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| [[Category:Topologists]]
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| [[Category:University of Wisconsin–Madison faculty]]
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| [[Category:Logicians]]
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| {{US-mathematician-stub}}
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Friends call him Royal. Arizona has usually been my living place but my spouse desires us to transfer. Bookkeeping has been his day occupation for a while. Playing crochet is something that I've done for years.
Take a look at my homepage: extended car warranty (please click the next site)