L'Axiome de la paire dans le système de Zermelo.
Using the theory of rudimentary recursion and provident sets expounded in [MB], we give a treatment of set forcing appropriate for working over models of a theory PROVI which may plausibly claim to be the weakest set theory supporting a smooth theory of set forcing, and of which the minimal model is Jensen’s . Much of the development is rudimentary or at worst given by rudimentary recursions with parameter the notion of forcing under consideration. Our development eschews the power set axiom. We...
We formulate, within the frame-theory for the foundations of Mathematics outlined in [2], a list of axioms which state that almost all "interesting" collections and almost all "interesting" operations are elements of the universe. The resulting theory would thus have the important foundational feature of being completely self-contained. Unfortunately, the whole list is inconsistent, and we are led to formulate the following problem, which we call the problem of self-reference: "Find out...