The nature of progress in mathematics: the significance of analogy

International audienceWhereas logic was traditionally regarded as a critical tool for the foundation or for the theoretical clarification of concepts, it has become "an effective tool for mathematical research". In particular, model theory has transformed logic into an art of invention. Examples borrowed from Tarski's work are given, namely the definability of subsets of real numbers (1931), which led to the concept of semi-algebraic set, and the quantifier elimination, which is the source of remarkable transfer principles