The algebraic geometers of the Italian school had often used the somewhat foggy concept of the generic point of an algebraic variety. What is true for the generic point is true for "most" points of the variety. In Weil's "Foundations of Algebraic Geometry" (1946), generic points are constructed by taking points in a very large algebraically closed field, called a "universal domain". Although this worked as a foundation, it was awkward: there were many different generic points for the same variety. (In the later theory of schemes, each algebraic variety has a single generic point.)