We present a rst order untyped axiomatization of mathematics where proofs are objects in the sense of Heyting-Kolmogorov functional interpretation. The consistency of this theory is open. Key-words: formalization of mathematics, set theory, functionnal interpretation of proofs, re ection, G odel's theorem, Tarski's theorem (R esum e : tsvp) [email protected] Unit e de recherche INRIA Rocqu...

DATA TYPE See DATA ABSTRACTION ABSTRACTION (The result of) a process of simplification, to describe something at a more general level than the level of detail seen from another point of view. This is often achieved by omitting details specific to individual cases or to methods of implementation. For example, a realtor’s description of a house may leave out architectural detail so that it is an ...