View source for Menachem Magidor

{{Short description|Israeli mathematician}}
{{Infobox scientist
| name              = Menachem Magidor
| native_name       = מנחם מגידור
| native_name_lang  = he
| image             = MenachemMagidor.jpg
| image_size        = 180px
| caption           = Magidor in 2006
| birth_date        = {{Birth date and age|1946|1|24}}
| birth_place       = [[Petah Tikva]], [[Mandatory Palestine]] (now Israel)
| nationality       = Israeli
| field             = [[Mathematician]]
| work_institution  = Hebrew University
| alma_mater        = [[Hebrew University]]
| doctoral_advisor  = [[Azriel Lévy]]
| doctoral_students = {{plainlist|1=
*[[Moti Gitik]]
*[[Anna Sfard]]
}}
| known_for         = [[Mathematical logic]], [[Axiomatic Set Theory|Set theory]], [[Large cardinal property]]
| prizes            = 
| footnotes         = 
| module            = {{Infobox officeholder | embed = yes
   | office1        = [[Association for Symbolic Logic|President of the ASL]]
   | term_start1    = 1996
   | term_end1      = 1998
   | predecessor1   = [[George Boolos]]
   | successor1     = [[Donald A. Martin]]
   | office2        = [[Hebrew University of Jerusalem|President of the Hebrew University of Jerusalem]]
   | term_start2    = 1997
   | term_end2      = 2009
   | predecessor2   = [[Hanoch Gutfreund]]
   | successor2     = [[Menachem Ben-Sasson]]
   | office3        = [[DLMPST|President of the DLMPST/IUHPST]]
   | term_start3    = 2016
   | term_end3      = 2019
   | predecessor3   = [[Elliott Sober]]
   | successor3     = [[Nancy Cartwright (philosopher)|Nancy Cartwright]]
 }}
}}

'''Menachem Magidor''' ({{Langx|he|מנחם מגידור}}; born January 24, 1946) is an Israeli [[mathematician]] who specializes in  [[mathematical logic]], in particular [[Axiomatic Set Theory|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 as president of the 
[[International Union of History and Philosophy of Science#DLMPST|Division for Logic, Methodology and Philosophy of Science and Technology of the International Union for History and Philosophy of Science]] (DLMPST/IUHPS) from 2016 to 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]].

== Biography ==
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]].<ref>{{MathGenealogy|id=24629}}</ref> He served as  president of the [[Hebrew University of Jerusalem]] from 1997 to 2009, following [[Hanoch Gutfreund]] and succeeded by [[Menachem Ben-Sasson]].<ref>{{cite web|url=https://new.huji.ac.il/en/page/454 |title=Office of the President &#124; האוניברסיטה העברית בירושלים &#124; The Hebrew University of Jerusalem |publisher=New.huji.ac.il |date=2017-09-01 |accessdate=2020-02-18}}</ref> The Oxford philosopher [[Ofra Magidor]] is his daughter.

== Mathematical theories ==
Magidor obtained several important consistency results on powers of [[singular cardinal]]s substantially developing the method of [[Forcing (mathematics)|forcing]]. He [[list of forcing notions#Magidor forcing|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 cardinal]]s he constructed models (1977) of set theory with first examples of nonregular [[ultrafilter]]s over very small cardinals (related to the famous Guilmann–[[H. Jerome Keisler|Keisler]] problem concerning existence of nonregular ultrafilters), even with the example of jumping cardinality of [[ultrapower]]s. He proved consistent that <math>\aleph_\omega</math> is strong limit, but <math>2^{\aleph_\omega}=\aleph_{\omega+2}</math>. He even strengthened the condition that  <math>\aleph_\omega</math> is strong limit to that [[generalised continuum hypothesis]] holds below <math>\aleph_\omega</math>. 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 lemma]]s. He proved that if [[zero sharp|0<sup>#</sup>]] does not exist then every [[primitive recursive]] closed set of ordinals is the union of countably many sets in <math>L</math>.

== Selected publications  ==
[[File:Menachem Magidor 1973 (de-bordered, as-is).jpg|thumb|240px|Menachem Magidor in 1973]]
* {{cite journal|title=On the singular cardinals problem. I|author=Magidor, Menachem|journal= [[Israel Journal of Mathematics]]|volume=28|year=1977|issue=1–2|pages=1–31|doi=10.1007/BF02759779|doi-access=free}}
* {{cite journal|title=On the singular cardinals problem. II|author=Magidor, Menachem|journal=[[Annals of Mathematics]] |series=2 |volume=106|year=1977|issue=3|pages=517–547|doi=10.2307/1971065|jstor=1971065}}
* {{cite journal|title=Martin's maximum, saturated ideals, and nonregular ultrafilters. I|author1=Foreman, Matthew |author1-link=Matthew Foreman |author2=Magidor, Menachem |author3=Shelah, Saharon | authorlink3=Saharon Shelah |name-list-style=amp |journal=[[Annals of Mathematics]] |series=2|year=1988|volume=127|issue=1|pages=1–47|doi=10.2307/1971415|jstor=1971415}}
* {{cite journal|title=Martin's maximum, saturated ideals, and nonregular ultrafilters|author1=Foreman, Matthew |author1-link=Matthew Foreman |author2=Magidor, Menachem |author3=Shelah, Saharon | authorlink3=Saharon Shelah |name-list-style=amp |journal=[[Annals of Mathematics]] |series=2|year=1988|volume=127|issue=3|pages=521–545|doi=10.2307/2007004|jstor=2007004}}
* {{cite journal|title=Large cardinals and definable counterexamples to the continuum hypothesis|author1=Foreman, Matthew |author1-link=Matthew Foreman |author2=Magidor, Menachem |name-list-style=amp |journal=[[Annals of Pure and Applied Logic]]|year=1995|volume=76|issue=1|pages=47–97|doi=10.1016/0168-0072(94)00031-W|doi-access=free}}

== References ==
{{commons category|Menachem Magidor (mathematician)}}
<references/>

{{s-start}}
{{s-aca}}
{{s-bef|before = [[Elliott Sober]]}}
{{s-ttl|title = [[International Union of History and Philosophy of Science#DLMPST|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)]]|years = 2016-2019}}
{{s-aft|after= [[Nancy Cartwright (philosopher)|Nancy Cartwright]]}}
{{s-end}}

{{Authority control}}

{{DEFAULTSORT:Magidor, Menachem}}
[[Category:1946 births]]
[[Category:Living people]]
[[Category:Academic staff of the Hebrew University of Jerusalem]]
[[Category:20th-century  Israeli mathematicians]]
[[Category:21st-century  Israeli  mathematicians]]
[[Category:Set theorists]]
[[Category:Presidents of universities in Israel]]