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...