Kenneth Kunen

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

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