James Baumgartner

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James Baumgartner

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

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

1971/72 he was visiting professor at Caltech.

He dealt with iterated forcing and, based on the work of Saharon Shelah, formulated the Proper Forcing Axiom (PFA), showed its relative consistency to ZFC and applied the PFA many times.

He proved the relative ZFC consistency of the theorem that every two -dense sets in the real numbers are order isomorphic. Another influential theorem by Baumgartner is his proof with András Hajnal of a partition relation of ordinal numbers.

He had been married since 1966 and had two sons.

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

Fonts

  • Applications of the Proper Forcing Axiom. In: The Handbook of set-theoretic topology. North-Holland, 1984, pp. 913-959.
  • Iterated forcing. In: Adrian Mathias (Ed.): Surveys in Set Theory. London Math. Society Lecture Note Series 87, 1983, pp. 1-59.
  • with András Hajnal : A proof (involving Martin´s axiom) of a partition relation. Fundamenta Mathematica, Volume 78, 1973, pp. 193-203.
  • with Andras Hajnal: Polarized partition relations. J. Symbolic Logic, Vol. 66, 2001, pp. 811-821.
  • All- dense sets of reals can be isomorphic. Fundamenta Mathematica, Volume 79, 1973, pp. 101-106.
  • A new class of order types. In: Annals of Mathematical Logic. Volume 9, 1976, pp. 187-222.
  • Ineffability properties of cardinals I. In: Infinite and Finite Sets. Keszthely (Hungary) 1973, Colloquia Mathematica Societatis János Bolyai, Volume 10, North-Holland, 1975, pp. 109-130.
  • with Leo Harrington , Eugene Kleinberg: Adding a closed unbounded set. In: Journal of Symbolic Logic. Volume 41, 1976, pp. 481-482.
  • Ineffability properties of cardinals II. In: Robert E. Butts, Jaakko Hintikka (Ed.): Logic, Foundations of Mathematics and Computability Theory. Reidel, 1977, pp. 87-106.
  • with Fred Galvin : Generalized Erdős cardinals and Zero Sharp. In: Annals of Mathematical Logic. Volume 15, 1978, pp. 289-313.
  • with Paul Erdős , Fred Galvin, Jean Larson: Colorful partitions of cardinal numbers. Can. J. Math., Vol. 31, 1979, pp. 524-541.
  • with Paul Erdős, 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.
  • with Karel Prikry : Singular cardinals and the generalized continuum hypothesis. American Mathematical Monthly, Volume 84, 1977, pp. 108-113.

Web links

  • obituary
  • Obituary, European Set Theory Society by Mirna Dzamonja, Jean Larson, Boban Velickovic.

Individual evidence

  1. ↑ James Baumgartner in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
personal data
SURNAME Baumgartner, James
ALTERNATIVE NAMES Baumgartner, James Earl (full name); Baumgartner, Jim (nickname)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH March 23, 1943
PLACE OF BIRTH Wichita, Kansas
DATE OF DEATH December 28, 2011