On Bourbaki's axiomatic system for set theory

In this paper we study the axiomatic system proposed by Bourbaki for the Theory of Sets in the Elements de Mathematique. We begin by examining the role played by the sign tau in the framework of its formal logical theory and then we show that the system of axioms for set theory is equivalent to Zermelo-Fraenkel system with the axiom of choice but without the axiom of foundation. Moreover, we study Grothendieck's proposal of adding to Bourbaki's system the axiom of universes for the purpose of considering the theory of categories. In this regard, we make some historical and epistemological remarks that could explain the conservative attitude of the Group.