Education
Stanford University.
mathematician university professor topologist
Stanford University.
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, -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 the Martin Axiom first fails at a singular cardinal and constructed under Companies of Honour 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.
Kunen received his Doctor of Philosophy in 1968 from Stanford University, where he was supervised by Dana Scott.