Some axioms for mathematics, with Gilles Dowek, Emilie Grienenberger, Gabriel Hondet and François Thiré, 19 pages, FSCD'21, LIPIcs 195.

The λΠ-calculus modulo theory is a logical framework in which many logical systems can be expressed as theories. We present such a theory, the theory U, where proofs of several logical systems can be expressed. Moreover, we identify a sub-theory of U corresponding to each of these systems, and prove that, when a proof in U uses only symbols of a sub-theory, then it is a proof in that sub-theory.