Menachem Magidor

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Menachem Magidor
Professor Menachem Magidor in Jerusalem, December 2006
Born	January 24, 1946 (1946-01-24) (age 62) Petah Tikva
Residence	Jerusalem, Israel
Nationality	Israel
Ethnicity	Jewish
Fields	Mathematician
Institutions	Hebrew University
Alma mater	Hebrew University
Doctoral advisor	Azriel Levy
Known for	Mathematical logic, Set theory, Large cardinal property

Menachem Magidor (born on January 24, 1946 in Petah Tikva) is an Israeli mathematician and a professor of mathematics at the Hebrew University of Jerusalem. His main research interest lies in mathematical logic, in particular in set theory. Since 1997 he is the President of the Hebrew University of Jerusalem.

He received his Ph.D. in 1973 from the Hebrew University (his thesis On Super Compact Cardinals was written under the supervision of Azriel Levy).

[edit] Selected publications and results

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 to the least supercompact cardinal (but not in the same time). He proved consistent that $\aleph_\omega$ is strong limit, but $2^{\aleph_\omega}=\aleph_{\omega+2}$ . He even strengthened the condition that $\aleph_\omega$ is strong limit to that GCH holds below $\aleph_\omega$ . Both proofs used the consistency of very large cardinals. With Matthew Foreman and Saharon Shelah they formulated and proved the consistency of Martin's Maximum, a provably maximal form of Martin's axiom.

He authors more than 60 research articles, including:

Magidor, Menachem (1977). "On the singular cardinals problem. I". Israel J. Math. 28 (1-2): 1-31.
Magidor, Menachem (1977). "On the singular cardinals problem. II". Ann. Math. (2) 106 (3): 517-547.
Foreman, Matthew; Magidor, Menachem and Shelah, Saharon (1988). "Martin's maximum, saturated ideals, and nonregular ultrafilters. I". Ann. of Math. (2) 127 (1): 1-47.
Foreman, Matthew; Magidor, Menachem and Shelah, Saharon (1988). "Martin's maximum, saturated ideals, and nonregular ultrafilters.". Ann. of Math. (2) 127 (3): 521-545.
Foreman, Matthew and Magidor, Menachem (1995). "Large cardinals and definable counterexamples to the continuum hypothesis". Annals of Pure and Applied Logic 76 (1): 47–97.