 These include classification of aleph-one categorical theories of groups and fields in 1971, which was very influential in the development of geometric stability theory.In 1976, he proved a result on quantifier elimination for p-adic fields from which a theory of semi-algebraic and subanalytic geometry for p-adic fields follows (in analogy with that for the real field) as shown by Jan Denef and Lou van den Dries and others.This quantifier elimination theorem was used by Jan Denef in 1984 to prove a conjecture of Jean-Pierre Serre on rationality of various p-adic Poincaré series, and subsequently these methods have been applied to prove rationality of a wide range of generating functions in group theory (e.g.