In memoriam, Richard Laver (1942-2012)

The celebrated set theorist Richard Laver passed away on the 19th of September 2012.Laver was known for  a large number of deep results in set theory and other subjects. In 1971 he proved a long standing conjecture  of Fraïssé which states that every descending sequence of countable order types, as well as every antichain in this class, is finite. Laver’s novel idea of using the Nash-Williams notion of a bqo to solve this problem has had  a longstanding influence on the classification problems in the theory of orders and elsewhere. Another brilliant result,  in 1976, was the consistency of the Borel conjecture which states that every strong measure zero is countable.  In his paper he introduced the notion of a countable support iteration which has had a strong influence on the theory of forcing. In the large cardinal theory, Laver discovered in 1978 the notions of  Laver’s diamond and  a Laver function for supercompact cardinals, which allowed him to prove the consistency relative to a supercompact  of a supercompact cardinals kappa whose super compactness is indestructible under the forcing which is (<kappa)-directed closed.  This method now forms a backbone of large cardinal forcing. Among his other celebrated results are the consistency  (jointly with Shelah) of CH with no aleph_2-Suslin trees, the infinite dimension version of the Halpern–Läuchli theorem  on colorings of perfect trees and his influential work on the braid group induced by elementary embeddings.

Richard Laver was born in 1942. After getting his PhD at the University of California, Berkeley in 1969, under the supervision of Ralph McKenzie,  he spent some time at UCLA and then the largest part of his career as  Professor and  later Emeritus Professor at the University of Colorado, Boulder. Richard has had 7 Ph.D. students, several of whom continue their careers as mathematicians. In spite of a long and difficult struggle against Parkinson’s disease,  Richard continued his mathematical work to the end of his life. We shall all miss the gentle man and his elegant mathematics.

Mirna Dzamonja and Boban Velickovic

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