Siddhesh Joshi (Editor)

Howard Jerome Keisler

Updated on
Share on FacebookTweet on TwitterShare on LinkedInShare on Reddit
Fields  Mathematics
Role  Mathematician

Name  Howard Keisler
Known for  Non-standard analysis
Doctoral advisor  Alfred Tarski
Howard Jerome Keisler Howard Jerome Keisler First Edition AbeBooks
Born  December 3, 1936 Seattle (1936-12-03)
Institutions  University of Wisconsin-Madison
Education  University of California, Berkeley (1961)
Awards  Guggenheim Fellowship for Natural Sciences, US & Canada
People also search for  Chen Chung Chang, Alfred Tarski, Joseph Sgro
Books  Elementary Calculus: An Infinite, Model Theory, Model theory for infinitary l, Continuous Model Theory, Model Theory of Stochasti

Doctoral students  Frederick Rowbottom

Howard Jerome Keisler (born 3 December 1936) is an American mathematician, currently professor emeritus at University of Wisconsin–Madison. His research has included model theory and non-standard analysis.

His Ph.D. advisor was Alfred Tarski at Berkeley; his dissertation is Ultraproducts and Elementary Classes (1961).

Following Abraham Robinson's work resolving what had long been thought to be inherent logical contradictions in the literal interpretation of Leibniz's notation that Leibniz himself had proposed, that is, interpreting "dx" as literally representing an infinitesimally small quantity, Keisler published Elementary Calculus: An Infinitesimal Approach, a first-year calculus textbook conceptually centered on the use of infinitesimals, rather than the epsilon, delta approach, for developing the calculus.

He is also known for extending the Henkin construction (of Leon Henkin) to what are now called Henkin–Keisler models.

He held the named chair of Vilas Professor of Mathematics at Wisconsin.

Among Keisler's graduate students, several have made notable mathematical contributions, including Frederick Rowbottom who discovered Rowbottom cardinals. Several others have gone on to careers in computer science research and product development, including: Michael Benedikt, a professor of computer science at the University of Oxford, Kevin J. Compton, a professor of computer science at the University of Michigan, Curtis Tuckey, a developer of software-based collaboration environments; Joseph Sgro, a neurologist and developer of vision processor hardware and software, and Edward L. Wimmers, a database researcher at IBM Almaden Research Center.

In 2012 he became a fellow of the American Mathematical Society.

His son Jeffrey Keisler is a Fulbright Distinguished Chair.


  • Chang, C. C.; Keisler, H. J. Continuous Model Theory. Annals of Mathematical Studies, 58, Princeton University Press, 1966. xii+165 pp.
  • Model Theory for Infinitary Logic, North-Holland, 1971
  • Chang, C. C.; Keisler, H. J. Model theory. Third edition. Studies in Logic and the Foundations of Mathematics, 73. North-Holland Publishing Co., Amsterdam, 1990. xvi+650 pp. ISBN 0-444-88054-2; 1st edition 1973; 2nd edition 1977
  • Elementary Calculus: An Infinitesimal Approach. Prindle, Weber & Schmidt, 1976/1986. Available online at [1].
  • An Infinitesimal Approach to Stochastic Analysis, American Mathematical Society Memoirs, 1984
  • Keisler, H. J.; Robbin, Joel. Mathematical Logic and Computability, McGraw-Hill, 1996
  • Fajardo, Sergio; Keisler, H. J. Model Theory of Stochastic Processes, Lecture Notes in Logic, Association for Symbolic Logic. 2002
  • References

    Howard Jerome Keisler Wikipedia