| Résume | In this talk we present a new approach to Goedel's program for a step by step extension of set theory. This new approach is based on Robinson's model-theoretic notion of model companionship. We show that set theory has (absolute) model companions and that these are the H_{\kappa^+}: the collections of sets of hereditarily cardinality less than \kappa^+, for \kappa a regular cardinal. We then present the solution to CH that this approach provides. Finally we justify this approach as a realization of Hilbert's idea of completeness for formal theories. |
