# Howard Jerome Keisler

### Quick Info

Seattle, Washington, USA

**Jerome Keisler**is an American mathematician whose work included model theory and non-standard analysis.

### Biography

**Jerome Keisler**was the son of Harry Keisler (1909-1950) and Marion Siegel (1911-1996), known as Minnie. Harry, born on 21 July 1909 in Philadelphia, Pennsylvania, was not given a middle name, so he changed his name to Harry Benton Keisler. He worked in the scrap steel industry, being a salesman at the time his son was born and becoming Vice President for the Dulien Steel Company. Minnie was born in the Bronx, New York. Harry and Minnie were married in Seattle, Washington on 6 March 1934. Jerome had a younger sister, Arleen Jean Keisler, born in Seattle, Washington in 1939. Harry Keisler began teaching his son mathematics when he was four years old. Sadly Harry Keisler died on 14 April 1950 when Jerome was thirteen years old. When he was at high school, Jerome loved mathematics but did not think that he could ever pursue a career in that subject [6]:-

Once he attended college, however, he was fascinated by how much he could accomplish from reasoning with mathematics.Jerome Keisler studied at the California Institute of Technology, graduating with the degree of Bachelor of Science in mathematics in 1959. We note that even while an undergraduate, he was undertaking research and publishing Abstracts of his results in the

*Notices*of the American Mathematical Society. For example he published Abstracts of

*The theory of models with generalized atomic formulas, I and II*submitted 6 October 1958 and

*On unions of relational systems*submitted 1 March 1959. These papers were introduced by Olga Taussky-Todd who taught Keisler at the California Institute of Technology. Later in 1959 he published in the

*Notices*Abstracts of

*Limit reduced products*,

*A mathematical characterization of elementary equivalence*, and

*A characterization of Horn*classes all three introduced by Roger Lyndon.

On 1 May 1959, Keisler married Lois J Hoffman in San Diego, California; she was three years younger than her husband. They moved to the University of California, Berkeley, where he undertook research advised by Alfred Tarski. Tarski had been fortunate to be in the United States when World War II broke out in 1939 since he was able to remain there and had been appointed to the University of California, Berkeley, in 1942, becoming Professor of Mathematics in 1949. His obituary in

*The Times*tells us about Tarski's students at Berkeley:-

His seminars at Berkeley fast became a power-house of logic. His students, many of them now distinguished mathematicians, recall the awesome energy with which he would coax and cajole their best work out of them, always demanding the highest standards of clarity and precision.Keisler's progress was rapid and his first paper appeared in print in 1960. This was a 26-page paper entitled

*Theory of models with generalized atomic formulas*which was published by the

*Journal of Symbolic Logic*. In this paper he gave a necessary and sufficient condition for an elementary class to be characterized by a set of sentences having a prescribed number of alternations of quantifiers. The paper was submitted on 28 April 1959 while he was still a student at the California Institute of Technology and this is the address on the paper. He gives the following acknowledgement:-

The author received many helpful suggestions and a great deal of encouragement in connection with this paper from C C Chang, Richard A Dean, and Roger C Lyndon.We note that Chen Chung Chang (1927-2014) collaborated with Keisler throughout his career and they wrote joint papers and books. Richard A Dean taught Keisler at the California Institute of Technology. Keisler was awarded a Ph.D. in 1961, after only two years of research at Berkeley, after submitting his 45-page thesis

*Ultraproducts and elementary classes*. He begins the Introduction to the thesis as follows:-

In the theory of models of the first order predicate logic with identity we study the relationship between notions from logic and purely mathematical objects, called relational systems, or (first order) structures, A, consisting of a set A and a sequence of relations on A corresponding to the predicate symbols of the logic. In such studies some of the most useful methods are those which permit us to form structures which have certain semantical properties. For example, the completeness theorem permits us to form a structure which satisfies a given consistent set of sentences.He gives the following Acknowledgement:-

A number of interesting discussions with C C Chang, Dana Scott, Robert Vaught, and my thesis advisor Alfred Tarski were of great value in the preparation of this manuscript.After the award of his Ph.D. in 1961, Keisler was appointed as a mathematician at the Institute for Defense Analysis in Princeton, New Jersey. He worked there until he was appointed as an assistant professor at the University of Wisconsin-Madison in 1962. He was promoted to associate professor in 1964 and in 1967 became a full professor serving in this position for 15 years. In 1982, Keisler was named William F Vilas professor at the University of Wisconsin-Madison. He continued to work at the University of Wisconsin-Madison for the rest of his career, retiring in 2002 having reached the age of 65.

Keisler attended the International Congress of Mathematicians held in Stockholm in August 1962. He travelled with his wife Lois J Keisler and they arrived back in New York on a flight from Oslo on 23 August 1962. They gave their address at that time as Sunset Hill, Princeton, New Jersey. In 1970 he was an invited plenary speaker at the International Congress of Mathematicians held in Nice, France, giving the talk

*Model Theory*. He began his talk as follows:-

Twenty years ago, A Robinson and A Tarski lectured on the subject of model theory to the International Congress at Cambridge, Massachusetts. At that time the subject was just beginning, and only two real theorems were known. Since then progress has been so spectacular that today it takes years of graduate study to reach the frontier. In this lecture I will try to give an idea of what the subject is like and where it is going. Model theory is a combination of universal algebra and logic.Keisler has written a number of books, some of which have run to several editions. We give some details, including extracts of reviews and prefaces, at THIS LINK.

In 2018 Keisler was presented with the Albert Nelson Marquis Lifetime Achievement Award by Marquis Who's Who. The citation reads:-

Marquis Who's Who, the world's premier publisher of biographical profiles, is proud to present Howard Jerome Keisler, PhD, with the Albert Nelson Marquis Lifetime Achievement Award. An accomplished listee, Dr Keisler celebrates many years' experience in his professional network, and has been noted for achievements, leadership qualities, and the credentials and successes he has accrued in his field. As in all Marquis Who's Who biographical volumes, individuals profiled are selected on the basis of current reference value. Factors such as position, noteworthy accomplishments, visibility, and prominence in a field are all taken into account during the selection process. ...Although Keisler retired in 2002, he certainly did not ease up on his outstanding publishing record with, up to February 2020, over 40 papers appearing in print from 2003 onwards.

Dr Keisler has made seminal contributions in mathematical logic, particularly in the areas of model theory and nonstandard analysis. He has authored or co-authored seven books in his field and more than 130 articles for scholarly journals. His published works include "Model Theory for Infinitary Logic" in 1971, "Model Theory" with C C Chang in 1973, in 1990, and in 2012, "An Infinitesimal Approach to Stochastic Analysis" in 1984, "Model Theory of Stochastic Processes" with Sergio Fajardo in 2002, and "Elementary Calculus: An Infinitesimal Approach" in 1976, in 1986 and in 2012. Dr Keisler is also a member and a former vice president of the Association of Symbolic Logic and a member of the American Mathematical Society.

An elected fellow of the American Mathematical Society, Dr Keisler accepted an Alfred P Sloan fellowship from 1966 to 1968. From 1976 to 1977, he completed a fellowship with the John Simon Guggenheim Foundation. Moreover, Dr Keisler has been selected for inclusion in many editions of Who's Who in America.

In recognition of outstanding contributions to his profession and the Marquis Who's Who community, Howard Jerome Keisler, PhD, has been featured on the Albert Nelson Marquis Lifetime Achievement website.

Finally let us note that Jerome and Lois Keisler's son Jeffrey M Keisler (born 1964) is a distinguished university professor. After the award of a BS with Honours and Distinction in Mathematics and Computer Science from the University of Wisconsin-Madison (1985), he received a MBA with High Honours in Business Economics from the University of Chicago (1996) and a PhD in Decision Sciences from Harvard University (1992). He is now (2020) Professor of Management Information Systems at the University of Massachusetts Boston. Jeffrey Keisler has published papers jointly with his father Jerome Keisler; for example

*Craig interpolation for networks of sentences*(2012) and

*Observing, reporting, and deciding in networks of sentences*(2014). Here is the Abstract of the 2014 paper:-

In prior work we considered networks of agents who prove facts from their knowledge bases and report them to their neighbours in their common languages in order to help a decider verify a single sentence. In report complete networks, the signatures of the agents and the links between agents are rich enough to verify any decider's sentence that can be proved from the combined knowledge base. This paper introduces a more general setting where new observations may be added to knowledge bases and the decider must choose a sentence from a set of alternatives. We consider the question of when it is possible to prepare in advance a finite plan to generate reports within the network. We obtain conditions under which such a plan exists and is guaranteed to produce the right choice under any new observations.

### References (show)

- E Bishop, Review: Elementary Calculus, An Approach Using Infinitesimals, by H Jerome Keisler,
*Bull. Amer. Math. Soc.***83**(2) (1977), 205-208. - J E Fenstad, Review: An infinitesimal approach to stochastic analysis, by H Jerome Keisler,
*The Journal of Symbolic Logic***51**(3) (1986), 822-824. - G Fuhrken, Review: Model theory, by Chen-chung Chang and H Jerome Keisler,
*The Journal of Symbolic Logic***41**(3) (1976), 697-699. - L Harkleroad, Review: Mathematical Logic and Computability (1996), by J Keisler and J Robbin,
*Modern Logic***8**(1-2) (1998), 138-141. - Howard Jerome Keisler, PhD, Presented with the Albert Nelson Marquis Lifetime Achievement Award by Marquis Who's Who,
*24-7pressrelease.com*(28 December 2018). https://www.24-7pressrelease.com/press-release/459385/howard-jerome-keisler-phd-presented-with-the-albert-nelson-marquis-lifetime-achievement-award-by-marquis-whos-who - Howard Jerome Keisler. Ph.D. Mathematics Educator (1 April 2019). https://whoswhonewsletters.com/2019/04/01/howard-jerome-keisler/
- P A Loeb, Review: Elementary Calculus, An Approach Using Infinitesimals, by H Jerome Keisler,
*The Journal of Symbolic Logic***46**(3) (1981), 673-676. - P J M, Review: Continuous model theory, by Chen-chung Chang and H Jerome Keisler,
*The Review of Metaphysics***20**(2) (1966), 364. - E W Madison and K D Stroyan, Review: Elementary Calculus, An Approach Using Infinitesimals, by H Jerome Keisler,
*Amer. Math. Monthly***84**(6) (1977), 496-500. - A Urquhart, Review: Model theory of stochastic processes, by Sergio Fajardo and H Jerome Keisler,
*The Bulletin of Symbolic Logic***10**(1) (2004), 110-112. - J Woleński, Review: Model theory (3rd ed.), by Chen-chung Chang and H Jerome Keisler,
*Studia Logica: An International Journal for Symbolic Logic***51**(1) (1992), 154-155.

### Additional Resources (show)

Other pages about Jerome Keisler:

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Written by J J O'Connor and E F Robertson

Last Update April 2020

Last Update April 2020