Abstract

A motivation and a presentation of the semantics of a formal system which proceeds from von neumann's "eine axiomatisierung der mengenlehre" by taking as fundamental notions the notion of partial functions, his principles of reification on the grounds of a "method of simulation" of meaningless terms and formulas by "ideal" terms and "virtual" formulas. theory of sets appears as the end of axiomatic extensions of the theory of objects (the intermediary extensions being the theories of classes, of universes, of aggregates).