Menachem Magidor
מנחם מגידור
Magidor in 2006
Born	(1946-01-24)January 24, 1946 (age 79) Petah Tikva,Mandatory Palestine (now Israel)
Alma mater	Hebrew University
Known for	Mathematical logic,Set theory,Large cardinal property
Scientific career
Fields	Mathematician
Institutions	Hebrew University
Doctoral advisor	Azriel Lévy
Doctoral students	Moti Gitik Anna Sfard
President of the ASL
In office 1996–1998
Preceded by	George Boolos
Succeeded by	Donald A. Martin
President of the Hebrew University of Jerusalem
In office 1997–2009
Preceded by	Hanoch Gutfreund
Succeeded by	Menachem Ben-Sasson
President of the DLMPST/IUHPST
In office 2016–2019
Preceded by	Elliott Sober
Succeeded by	Nancy Cartwright

Menachem Magidor (Hebrew:מנחם מגידור; born January 24, 1946) is an Israelimathematician who specializes inmathematical logic, in particularset theory. He served as president of theHebrew University of Jerusalem, was president of theAssociation for Symbolic Logic from 1996 to 1998 and as president of theDivision 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 theSolomon Bublick Award.

Menachem Magidor was born inPetah Tikva, Israel. He received hisPh.D. in 1973 from theHebrew University of Jerusalem. His thesis,On Super Compact Cardinals, was written under the supervision ofAzriel Lévy.^[1] The Oxford philosopherOfra Magidor is his daughter.

Magidor obtained several important consistency results on powers ofsingular cardinals, substantially developing the method offorcing. Hegeneralized thePrikry forcing in order to change thecofinality of alarge cardinal to a predeterminedregular cardinal. He proved that the leaststrongly compact cardinal can be equal to the leastmeasurable cardinal or the leastsupercompact cardinal, but not to both.

Assuming the consistency ofhuge cardinals, he constructed models (1977) of set theory with the first examples of nonregularultrafilters over very small cardinals (related to the famous Guilmann–Keisler problem concerning existence of nonregular ultrafilters), even with the example of jumping cardinality ofultrapowers. He proved that it is consistent with${\displaystyle 2^{{\mathrm{\aleph }}_{\omega }}={\mathrm{\aleph }}_{\omega +2}}$ for${\displaystyle {\mathrm{\aleph }}_{\omega }}$ to be strong limit, and strengthened the condition that${\displaystyle {\mathrm{\aleph }}_{\omega }}$ is strong limit to the condition that thegeneralised continuum hypothesis holds below${\displaystyle {\mathrm{\aleph }}_{\omega }}$. This constituted a negative solution to thesingular cardinals hypothesis. Both proofs used the consistency of very large cardinals.

Magidor,Matthew Foreman, andSaharon Shelah formulated and proved the consistency ofMartin's maximum, a provably maximal form ofMartin's axiom. Magidor also gave a simple proof of the Jensen and the Dodd–Jensencovering lemmas. He proved that if0^# does not exist, then everyprimitive recursive closed set of ordinals is the union of countably many sets in${\displaystyle L}$.

He served as president of theHebrew University of Jerusalem from 1997 to 2009, followingHanoch Gutfreund and succeeded byMenachem Ben-Sasson.^[2]

• Magidor, Menachem (1977)."On the singular cardinals problem. I".Israel Journal of Mathematics.28 (1–2):1–31.doi:10.1007/BF02759779.
• Magidor, Menachem (1977). "On the singular cardinals problem. II".Annals of Mathematics. 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".Annals of Mathematics. 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".Annals of Mathematics. 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.

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