this paper is clearly stated, after recalling how the logical connectives can be explained in term of the Sheffer connective: "We are led to the idea, which at first glance certainly appears extremely bold of attempting to eliminate by suitable reduction the remaining fundamental notions, those of proposition, propositional function, and variable, from those contexts in which we are dealing with completely arbitrary, logical general propositions . . . To examine this possibility more closely and to pursue it would be valuable not only from the methodological point of view that enjoins us to strive for the greatest possible conceptual uniformity but also from a certain philosophic, or if you wish, aesthetic point of view."

The axiomofchoice and the law of excluded middle in weak set theories

The goal of this note is to extend Gandy’s interpretability result [2] of extensional type theory in intensional type theory for simple type theory, to a dependent type system with one universe. For simple type theory, Gandy observed that any definable term is extensional. As formulated in [2], this reflects the fact that “the mathematician believes that the complex quantities which