- James Earl Baumgartner
James Earl Baumgartner (1943) is an American
mathematician active inset theory ,mathematical logic and foundations, andtopology . He is an emeritus professor atDartmouth 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 wasRobert 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 thepartition relation omega_1 o(alpha)^2_n holds for alpha. 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), 1990References
Wikimedia Foundation. 2010.