In the world of *Kenneth Kunen*, we can find a wide variety of situations, opinions and experiences that lead us to question and reflect on different aspects of life. Whether through observation, participation or research, *Kenneth Kunen* gives us the opportunity to explore new horizons and discover valuable information that can enrich our knowledge. Throughout history, *Kenneth Kunen* has played a fundamental role in the development of society, and its influence continues to be relevant today. In this article, we will explore the different facets of *Kenneth Kunen* and analyze its impact on contemporary society.

Kenneth Kunen | |
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Born | Herbert Kenneth Kunen August 2, 1943 |

Died | August 14, 2020 | (aged 77)

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 |

Thesis | Inaccessibility Properties of Cardinals (1968) |

Doctoral advisor | Dana Scott |

**Herbert Kenneth Kunen** (August 2, 1943 – August 14, 2020^{[1]}) was a professor of mathematics at the University of Wisconsin–Madison^{[2]} 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.

Kunen was born in New York City in 1943 and died in 2020.^{[1]} He lived in Madison, Wisconsin, with his wife Anne, with whom he had two sons, Isaac and Adam.^{[3]}

Kunen completed his undergraduate degree at the California Institute of Technology^{[3]} and received his Ph.D. in 1968 from Stanford University, where he was supervised by Dana Scott.^{[4]}

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 , 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.

The journal *Topology and its Applications* has dedicated a special issue to "Ken" Kunen,^{[3]} containing a biography by Arnold W. Miller, and surveys about Kunen's research in various fields by Mary Ellen Rudin, Akihiro Kanamori, István Juhász, Jan van Mill, Dikran Dikranjan, and Michael Kinyon.

*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.^{[5]}- (co-edited with Jerry E. Vaughan).
*Handbook of Set-Theoretic Topology*. North-Holland, 1984. ISBN 0-444-86580-2.^{[6]}

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^{a}^{b}"In Memoriam: Ken Kunen".*Department of Mathematics, University of Wisconsin–Madison*. 17 August 2020. **^**"UW Department of Mathematics Emeriti". Archived from the original on 2008-12-09. Retrieved 2008-10-08.- ^
^{a}^{b}^{c}Hart, Joan, ed. (1 Dec 2011). "Special Issue: Ken Kunen".*Topology and Its Applications*.**158**(18): 2443–2564. **^**Kenneth Kunen at the Mathematics Genealogy Project**^**Henson, C. Ward (1984). "Review:*Set theory, an introduction to independence proofs*, by Kenneth Kunen" (PDF).*Bull. Amer. Math. Soc. (N.S.)*.**10**(1): 129–131. doi:10.1090/s0273-0979-1984-15214-5.**^**Baldwin, Stewart (December 1987). "Review:*Handbook of set-theoretic topology*edited by Kenneth Kunen and Jerry E. Vaughan".*Journal of Symbolic Logic*.**52**(4): 1044–1045. doi:10.2307/2273837. JSTOR 2273837.

- Kunen's home page
- "In Memory of Ken Kunen" (PDF).
*Notices of the American Mathematical Society*.**69**(10): 1758–1769. November 2022. doi:10.1090/noti2570.