Some Axioms for Mathematics

Authors Frédéric Blanqui , Gilles Dowek , Émilie Grienenberger, Gabriel Hondet, François Thiré

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Author Details

Frédéric Blanqui
  • Université Paris-Saclay, ENS Paris-Saclay, LMF, CNRS, Inria, France
Gilles Dowek
  • Université Paris-Saclay, ENS Paris-Saclay, LMF, CNRS, Inria, France
Émilie Grienenberger
  • Université Paris-Saclay, ENS Paris-Saclay, LMF, CNRS, Inria, France
Gabriel Hondet
  • Université Paris-Saclay, ENS Paris-Saclay, LMF, CNRS, Inria, France
François Thiré
  • Nomadic Labs, Paris, France


The authors want to thank Michael Färber, César Muñoz, Thiago Felicissimo, and Makarius Wenzel for helpful remarks on a first version of this paper.

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Frédéric Blanqui, Gilles Dowek, Émilie Grienenberger, Gabriel Hondet, and François Thiré. Some Axioms for Mathematics. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
  • Theory of computation → Type theory
  • Theory of computation → Equational logic and rewriting
  • logical framework
  • axiomatic theory
  • dependent types
  • rewriting
  • interoperabilty


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