James Earl Baumgartner Biography, Age, Height, Wife, Net Worth and Family

One of Baumgartner’s results is the consistency of the statement that any two ℵ 1 {\displaystyle \aleph _{1}} -dense sets of reals are order isomorphic (a set of reals is ℵ 1 {\displaystyle \aleph _{1}} -dense if it has exactly ℵ 1 {\displaystyle \aleph _{1}} points in every open interval). With András Hajnal he proved the Baumgartner–Hajnal theorem, which states that the partition relation ω 1 → ( α ) n 2 {\displaystyle \omega _{1}\to (\alpha )_{n}^{2}} holds for α < ω 1 {\displaystyle \alpha <\omega _{1}} and n < ω {\displaystyle n<\omega } . He died in 2011 of a heart attack at his home in Hanover, New Hampshire.

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 spent there his entire career.

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