Dear members, it has recently been put forth to me the question as to when and by which means did it become clear to the majority of logicians and mathematicians that set theory prevailed over Russell's theory of types (as in Principia)? (By set theory I mean as in the axioms of Zermelo-Fraenkel's or ZFC, NBG etc.) Not being an expert, I wasn't exactly secure as to how to answer this question. Both Whitehead-Russell's and Zermelo-Fraenkel's axioms are victims to Gödel's second Incompleteness theorem, with the difference that the consistency of ZFC can be proved by assuming the existence of an inaccessible cardinal. What are your views on this?