James Earl Baumgartner

James Earl Baumgartner (1943) is an American mathematician active in set theory, mathematical logic and foundations, and topology. He is an emeritus professor at Dartmouth College.

Baumgartner received his PhD in 1970 from the University of California, Berkeley for a dissertation entitled "Results and Independence Proofs in Combinatorial Set Theory". His advisor was Robert Vaught. [MathGenealogy|id=22587]

One of Baumgartner's result 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 Andras Hajnal he proved the result that the partition relation $omega\_1\; o(alpha)^2\_n$ holds for

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 Erdos 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