Menachem Magidor

Magidor obtained several important consistency results on powers of singular cardinals, substantially developing the method of forcing. He generalized the Prikry forcing in order to change the cofinality of a large cardinal to a predetermined regular cardinal. He proved that the least strongly compact cardinal can be equal to the least measurable cardinal or the least supercompact cardinal, but not to both.

Assuming the consistency of huge cardinals, he constructed models (1977) of set theory with the first examples of nonregular ultrafilters over very small cardinals (related to the famous Guilmann–Keisler problem concerning existence of nonregular ultrafilters), even with the example of jumping cardinality of ultrapowers. He proved that it is consistent with

2

ℵ

ω

=

ℵ

ω

+

2

{\displaystyle 2^{\aleph _{\omega }}=\aleph _{\omega +2}}

for

ℵ

ω

{\displaystyle \aleph _{\omega }}

to be strong limit, and strengthened the condition that

ℵ

ω

{\displaystyle \aleph _{\omega }}

is strong limit to the condition that the generalised continuum hypothesis holds below

ℵ

ω

{\displaystyle \aleph _{\omega }}

. This constituted a negative solution to the singular cardinals hypothesis. Both proofs used the consistency of very large cardinals.

Magidor, Matthew Foreman, and Saharon Shelah formulated and proved the consistency of Martin's maximum, a provably maximal form of Martin's axiom. Magidor also gave a simple proof of the Jensen and the Dodd–Jensen covering lemmas. He proved that if 0# does not exist, then every primitive recursive closed set of ordinals is the union of countably many sets in

L

{\displaystyle L}

.

He served as president of the Hebrew University of Jerusalem from 1997 to 2009, following Hanoch Gutfreund and succeeded by Menachem Ben-Sasson.

Menachem Magidor was born in Petah Tikva, Israel. He received his Ph.D. in 1973 from the Hebrew University of Jerusalem. His thesis, On Super Compact Cardinals, was written under the supervision of Azriel Lévy. The Oxford philosopher Ofra Magidor is his daughter.