Menachem Magidor

Menachem Magidor (Hebrew: מנחם מגידור; born January 24, 1946) is an Israeli mathematician who specializes in mathematical logic, in particular set theory. He served as President of the Hebrew University of Jerusalem, was President of the Association for Symbolic Logic from 1996 to 1998, and is currently the President of the Division for Logic, Methodology and Philosophy of Science and Technology of the International Union for History and Philosophy of Science (DLMPST/IUHPS; 2016-2019). In 2016 he was elected an honorary foreign member of the American Academy of Arts and Sciences. In 2018 he received the Solomon Bublick Award.

Menachem Magidor
MenachemMagidor.jpg
Professor Menachem Magidor in Jerusalem (December 2006)
Born (1946-01-24) January 24, 1946 (age 74)
NationalityIsraeli
Alma materHebrew University
Known forMathematical logic, Set theory, Large cardinal property
Scientific career
FieldsMathematician
InstitutionsHebrew University
Doctoral advisorAzriel Lévy
Doctoral studentsMoti Gitik
President of the ASL
In office
1996–1998
Preceded byGeorge Boolos
Succeeded byDonald A. Martin
President of the Hebrew University of Jerusalem
In office
1997–2009
Preceded byHanoch Gutfreund
Succeeded byMenachem Ben-Sasson
President of the DLMPST/IUHPST
In office
2016–2019
Preceded byElliott Sober
Succeeded byNancy Cartwright

BiographyEdit

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.[1] He served as President of the Hebrew University of Jerusalem from 1997 to 2009, following Hanoch Gutfreund and succeeded by Menachem Ben-Sasson.[2] The Oxford philosopher Ofra Magidor is his daughter.

Mathematical theoriesEdit

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 at the same time). Assuming consistency of huge cardinals he constructed models (1977) of set theory with 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 consistent that   is strong limit, but  . He even strengthened the condition that   is strong limit to that GCH holds below  . 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  .

Selected published worksEdit

 
Menachem Magidor in 1973
  • Magidor, Menachem (1977). "On the singular cardinals problem. I". Israel J. Math. 28 (1–2): 1–31. doi:10.1007/BF02759779.
  • Magidor, Menachem (1977). "On the singular cardinals problem. II". Ann. of Math. 2. 106 (3): 517–547. doi:10.2307/1971065. JSTOR 1971065.
  • Foreman, Matthew; Magidor, Menachem & Shelah, Saharon (1988). "Martin's maximum, saturated ideals, and nonregular ultrafilters. I". Ann. of Math. 2. 127 (1): 1–47. doi:10.2307/1971415. JSTOR 1971415.
  • Foreman, Matthew; Magidor, Menachem & Shelah, Saharon (1988). "Martin's maximum, saturated ideals, and nonregular ultrafilters". Ann. of Math. 2. 127 (3): 521–545. doi:10.2307/2007004. JSTOR 2007004.
  • Foreman, Matthew & Magidor, Menachem (1995). "Large cardinals and definable counterexamples to the continuum hypothesis". Annals of Pure and Applied Logic. 76 (1): 47–97. doi:10.1016/0168-0072(94)00031-W.

ReferencesEdit

Academic offices
Preceded by
Elliott Sober
President of the Division for Logic, Methodology and Philosophy of Science and Technology of the International Union for History and Philosophy of Science and Technology (DLMPST/IUHPST)
2016-2019
Succeeded by
Nancy Cartwright