James Earl Baumgartner

James "Jim" Earl Baumgartner ( born March 23, 1943 in Wichita (Kansas ), † 28 December 2011) was an American mathematician who dealt with axiomatic set theory and the foundations of mathematics.

Baumgartner studied at Caltech with a bachelor 's degree in 1960 and in 1970 received his doctorate at the University of California, Berkeley with Robert Vaught ( Results and Independence Proofs in Combinatorial Set Theory ). In 1969 he was instructor, assistant professor in 1971, associate professor in 1976 and professor in 1980 at Dartmouth College. From 1983, he was there, John G. Kemeny Parents' professor. In 1982 he was diagnosed with multiple sclerosis, which eventually forced him into the wheelchair. He died of a heart attack.

1971/72 he was a visiting professor at Caltech.

He dealt with iteriertem Forcing and formulated building on the work of the Proper Forcing Axiom Saharon Shelah (PFA ), showed its relative consistency of ZFC and turned the PFA often to.

He proved the relative consistency of ZFC - set that any two - dense set are properly isomorphic to the real numbers. Another influential theorem of Baumgartner 's his proof with András Hajnal a partition ratio of ordinals.

He was married in 1966 and had two sons.

His doctoral included Stan Wagon, Jean Larson, Tadatoshi Miyamoto and Alan D. Taylor.

Writings

  • Applications of the Proper Forcing Axiom, in the Handbook of set - theoretic topology, North -Holland, 1984, pp. 913-959
  • Iterated forcing, in Adrian Mathias (Editor) Surveys in Set Theory, London Mathematical Society Lecture Note Series 87, 1983, pp. 1-59
  • Andras Hajnal with: A proof (Involving Martin's axiom ) of a partition relation, Fundamenta Mathematica, Volume 78, 1973, p 193-203
  • All- dense sets of reals can be isomorphic, Fundamenta Mathematica, Volume 79, 1973, p 101-106
  • A new class of order types, Annals of Mathematical Logic, Volume 9, 1976, p 187-222
  • Ineffability properties of cardinals I, in: Infinite and Finite Sets, Keszthely ( Hungary) in 1973, Colloquia Mathematica Societatis János Bolyai, Vol 10, North -Holland, 1975, p 109-130
  • Leo Harrington, Eugene Kleinberg: Adding a closed unbounded set, Journal of Symbolic Logic, Volume 41, 1976, p 481-482
  • Ineffability properties of cardinals II, in: Robert E. Butts, Jaakko Hintikka, (Eds. ), Logic, Foundations of Mathematics and Computability Theory, Reidel, 1977, pp. 87-106
  • Fred Galvin, Generalized Erdős cardinals and Zero Sharp, Annals of Mathematical Logic, Volume 15, 1978, p 289-313
  • Paul Erdos, Fred Galvin, Jean Larson: Colorful partitions of cardinal numbers, Can. J. Math, Volume 31, 1979, pp. 524-541
  • Paul Erdos, D. Higgs: Cross -cuts in the power set of an infinite set, Order 1, 1984, pp. 139-145
  • As editor: Axiomatic Set Theory, Contemporary Mathematics, Volume 31, 1990
  • Karel Prikry: Singular cardinals and the generalized continuum hypothesis, American Mathematical Monthly, Volume 84, 1977, p 108-113
December 28 Set theory#Axiomatic set theory Robert Lawson Vaught Mathematics Genealogy Project
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