James Earl Baumgartner

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.

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