Kenneth Kunen

Herbert Kenneth Kunen (August 2, 1943 – August 14, 2020 ) was a professor of mathematics at the University of Wisconsin–Madison who worked in set theory and its applications to various areas of mathematics, such as set-theoretic topology and measure theory. He also worked on non-associative algebraic systems, such as loops, and used computer software, such as the Otter theorem prover, to derive theorems in these areas.

Personal life Kunen was born in New York City in 1943 and died in 2020.

Career and research 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, -saturated ideal on from the consistency of the existence of a huge cardinal. He introduced the method of iterated ultrapowers, with which he proved that if is a measurable cardinal with or is a strongly compact cardinal then there is an inner model of set theory with many measurable cardinals. He proved Kunen's inconsistency theorem showing the impossibility of a nontrivial elementary embedding with the axiom of choice, 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 Martin's axiom first fails at a singular cardinal and constructed under the continuum hypothesis a compact L-space supporting a nonseparable measure. He also showed that has no increasing chain of length in the standard Cohen model where the continuum is . The concept of a Jech–Kunen tree is named after him and Thomas Jech.