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Two Classical Surprises Concerning the Axiom of Choice and the Continuum Hypothesis

by Leonard Gillman

Award: Lester R. Ford

Year of Award: 2003

Publication Information: The American Mathematical Monthly, vol. 109, 2002, pp. 544-553

Summary: This paper introduces the reader to two remarkable results in the theory of sets. Both are more than fifty years old, but neither one appears to be well known among nonspecialists. Each one states that a certain proposition implies the Axiom of Choice.

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About the Author: The American Mathematical Monthly, (2002)) Leonard Gillman held a piano fellowship at the Juilliard Graduate School for five years before spending nine years in Naval Operations Research and then completing his Ph.D. at Columbia University in transfinite numbers under the direction of E. R. Lorch and the unofficial direction of Alfred Tarski (UC Berkeley). He then taught at Purdue, Rochester, and Texas for a total of thirty-five years (including two on leave at the Institute for Advanced Study), retiring in 1987. He is the author of two MAA booklets, You'll Need Math (1967), for high school students, and Writing Mathematics Well (1987), for authors; coauthor with R. H. McDowell of a calculus text (1973, 1978), and coauthor with Meyer Jerison of Rings of Continuous Functions (1960, 1976), a graduate text. He was MAA Treasurer for thirteen years (1973-86) and President for the canonical two (1987-89). He received a Lester R. Ford award for his paper "An axiomatic approach to the integral" in this MONTHLY (January 1993, pp. 16-25) and the 1999 Gung-Hu Award for Distinguished Service to Mathematics. He has performed at the piano at five national meetings and several MAA section meetings.

 

Subject classification(s): Index | Logic and Foundations | Set Theory
Publication Date: 
Tuesday, September 23, 2008

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