James Earl Baumgartner

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 for a dissertation titled Results and Independence Proofs in Combinatorial Set Theory. His advisor was Robert Vaught. He became a professor at Dartmouth College in 1969, and spent his entire career there. One of Baumgartner's results is the consistency of the statement that any two ℵ1-dense sets of reals are order isomorphic (a set of reals is ℵ1-dense if it has exactly ℵ1 points in every open interval). With András Hajnal he proved the Baumgartner–Hajnal theorem, which states that the partition relation ω1→(α)n2 holds for α<ω1 and n<ω. He died in 2011 of a heart attack at his home in Hanover, New Hampshire.