Kenneth Kunen

Kenneth Kunen
Born	Herbert Kenneth Kunen (1943-08-02)August 2, 1943
Nationality	American
Alma mater	California Institute of Technology Stanford University
Known for	set theory, set-theoretic topology, non-associative algebraic systems
Scientific career
Fields	Mathematics
Institutions	University of Wisconsin–Madison
Doctoral advisor	Dana Scott

Herbert Kenneth Kunen (born August 2, 1943) is an emeritus professor of mathematics at the University of Wisconsin–Madison 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 non-associative algebraic systems, such as loops, and uses computer software, such as the Otter theorem prover, to derive theorems in these areas.

Kunen showed that if there exists a nontrivial elementary embedding j:L→L of the constructible universe, then 0^# exists. He proved the consistency of a normal, $\aleph _{2}$-saturated ideal on $\aleph _{1}$ from the consistency of the existence of a huge cardinal. He introduced the method of iterated ultrapowers, with which he proved that if $\kappa$ is a measurable cardinal with $2^{\kappa }>\kappa ^{+}$ or $\kappa$ is a strongly compact cardinal then there is an inner model of set theory with $\kappa$ many measurable cardinals. He proved Kunen's inconsistency theorem showing the impossibility of a nontrivial elementary embedding $V\to V$, which had been suggested as a large cardinal assumption (a Reinhardt cardinal).

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 under CH a compact L-space supporting a nonseparable measure. He also showed that $P(\omega )/Fin$ has no increasing chain of length $\omega _{2}$ in the standard Cohen model where the continuum is $\aleph _{2}$. The concept of a Jech–Kunen tree is named after him and Thomas Jech.

Kunen completed his undergraduate degree at the California Institute of Technology and received his Ph.D. in 1968 from Stanford University, where he was supervised by Dana Scott.

Selected publications

• Set Theory. College Publications, 2011. ISBN 978-1848900509.
• The Foundations of Mathematics. College Publications, 2009. ISBN 978-1-904987-14-7.
• Set Theory: An Introduction to Independence Proofs. North-Holland, 1980. ISBN 0-444-85401-0.
• (co-edited with Jerry E. Vaughan). Handbook of Set-Theoretic Topology. North-Holland, 1984. ISBN 0-444-86580-2.

Personal life

Kunen was born in New York in 1943. He lives in Madison, Wisconsin with his wife Anne. They have two sons, Isaac and Adam.

Bibliography

The journal Topology and its Applications has dedicated a special issue to "Ken" Kunen, containing a biography by Arnold W. Miller, and surveys about Kunen research in various fields by Mary Ellen Rudin, Akihiro Kanamori, István Juhász, Jan van Mill, Dikran Dikranjan, and Michael Kinyon.

External links

• Kunen's home page