James Earl Baumgartner
Encyclopedia
James Earl Baumgartner 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.
One of Baumgartner's results is the consistency of the statement that any two
-dense sets of reals are order isomorphic (a set of reals is 
-dense if it has exactly 
points in every open interval). With András Hajnal
he proved the result (Baumgartner–Hajnal theorem) that the partition relation
holds for 
.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
active in set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
, mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
and foundations, and topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
. He is an emeritus professor at Dartmouth College
Dartmouth College
Dartmouth College is a private, Ivy League university in Hanover, New Hampshire, United States. The institution comprises a liberal arts college, Dartmouth Medical School, Thayer School of Engineering, and the Tuck School of Business, as well as 19 graduate programs in the arts and sciences...
.
Baumgartner received his PhD in 1970 from the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
for a dissertation entitled Results and Independence Proofs in Combinatorial Set Theory. His advisor was Robert Vaught.
One of Baumgartner's results is the consistency of the statement that any two
-dense sets of reals are order isomorphic (a set of reals is -dense if it has exactly points in every open interval). With András HajnalAndrás Hajnal
András Hajnal is an emeritus professor of mathematics at Rutgers University and a member of the Hungarian Academy of Sciences known for his work in set theory and combinatorics.-Biography:Hajnal was born on 13 May 1931, in Hungary....
he proved the result (Baumgartner–Hajnal theorem) that the partition relation
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, LeoLeo HarringtonLeo Anthony Harrington is a professor of mathematics at the University of California, Berkeley who works inrecursion theory, model theory, and set theory.* Harrington and Jeff Paris proved the Paris–Harrington theorem....
; 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, FredFred GalvinFrederick William Galvin is a mathematician, currently a professor at the University of Kansas. His research interests include set theory and combinatorics.His notable combinatorial work includes the proof of the Dinitz conjecture...
, Generalized Erdos cardinals and 0#Zero sharpIn the mathematical discipline of set theory, 0# is the set of true formulas about indiscernibles in the Gödel constructible universe. It is often encoded as a subset of the integers , or as a subset of the hereditarily finite sets, or as a real number...
, Annals of Mathematical Logic 15, 289–313, 1978 - Baumgartner, James E.; Erdős, PaulPaul ErdosPaul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
; 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