James Earl Baumgartner

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James Earl Baumgartner
James Baumgartner in 1975
Born	(1943-03-23)March 23, 1943 Wichita, Kansas
Died	December 28, 2011(2011-12-28) (aged 68)
Nationality	American
Fields	Mathematics
Institutions	Dartmouth College
Alma mater	University of California, Berkeley
Doctoral advisor	Robert Lawson Vaught
Doctoral students	Jean Larson Alan D. Taylor Stanley Wagon

James Earl Baumgartner (March 23, 1943 – December 28, 2011) was an American mathematician who worked in set theory, mathematical logic and foundations, and topology.^[1]

Baumgartner was born in Wichita, Kansas, began his undergraduate study at the California Institute of Technology in 1960, then transferred to the University of California, Berkeley, from which he received his PhD in 1970 from for a dissertation entitled Results and Independence Proofs in Combinatorial Set Theory. His advisor was Robert Vaught.^[2] He became a professor at Dartmouth College in 1969, and there spent his entire career.

One of Baumgartner's results is the consistency of the statement that any two $\aleph _{1}$ -dense sets of reals are order isomorphic (a set of reals is $\aleph _{1}$ -dense if it has exactly $\aleph _{1}$ points in every open interval). With András Hajnal he proved the result (Baumgartner–Hajnal theorem) that the partition relation $\omega _{1}\to (\alpha )_{n}^{2}$ holds for $\alpha <\omega _{1},n<\omega$ . He died of a heart attack in 2011.^[3]

Selected publications

Baumgartner, James E., A new class of order types, Annals of Mathematical Logic, 9:187–222, 1976
Baumgartner, James E., Ineffability properties of cardinals I, Infinite and Finite Sets, Keszthely (Hungary) 1973, volume 10 of Colloquia Mathematica Societatis János Bolyai, pages 109–130. North-Holland, 1975
Baumgartner, James E.; Harrington, Leo; Kleinberg, Eugene, Adding a closed unbounded set, Journal of Symbolic Logic, 41(2):481–482, 1976
Baumgartner, James E., Ineffability properties of cardinals II, Robert E. Butts and Jaakko Hintikka, editors, Logic, Foundations of Mathematics and Computability Theory, pages 87–106. Reidel, 1977
Baumgartner, James E.; Galvin, Fred, Generalized Erdős cardinals and 0^#, Annals of Mathematical Logic 15, 289–313, 1978
Baumgartner, James E.; Erdős, Paul; Galvin, Fred; Larson, J., Colorful partitions of cardinal numbers, Can. J. Math. 31, 524–541, 1979
Baumgartner, James E.; Erdős, Paul; Higgs, D., Cross-cuts in the power set of an infinite set, Order 1, 139–145, 1984
Baumgartner, James E. (Editor), Axiomatic Set Theory (Contemporary Mathematics, Volume 31), 1990

References

↑ "James E. Baumgartner Obituary". Rand-wilson.com. Retrieved 2012-01-06.
↑ James Earl Baumgartner at the Mathematics Genealogy Project
↑

Valley News obituary

Authority control	VIAF: 64254289 ISNI: 0000 0001 1659 0656 BNF: cb145924241 MGP: 22587

Persondata
Name	Baumgartner, James Earl
Alternative names
Short description	American logician
Date of birth	March 23, 1943
Place of birth	Wichita, Kansas
Date of death	December 28, 2011
Place of death

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