Constructively Finite?

Arnaud Spiwack (1, 2) , Thierry Coquand (3)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 TYPICAL - Types, Logic and computing
3 CSE - Department of Computer Science and Engineering [Göteborg]

This articles plays with several properties of Bishop sets which would be equivalent in ZFC to being finite. One of which is new. This is an occasion to analyse finely the different properties of finite sets and how they (constructively) relate to one another. We close this article by presenting a few well-known algorithms on finite structures, and describe which kind of finiteness they require.

Mots clés: Constructive mathematics

Domaines: Logique en informatique [cs.LO]; Catégories et ensembles [math.CT]

Arnaud Spiwack, Thierry Coquand. Constructively Finite?. Lambán Pardo, Laureano and Romero Ibáñez, Ana and Rubio García, Julio. Contribuciones científicas en honor de Mirian Andrés Gómez, Universidad de La Rioja, pp.217-230, 2010, 978-84-96487-50-5. ⟨inria-00503917⟩