Constructive theory of ordinals - Archive ouverte HAL Accéder directement au contenu
Chapitre D'ouvrage Année : 2022

Constructive theory of ordinals

Thierry Coquand
  • Fonction : Auteur
  • PersonId : 864710

Résumé

In Chapter 3 of his Notes on constructive mathematics, Martin-Löf describes recursively constructed ordinals. He gives a constructively acceptable version of Kleene's computable ordinals. In fact, the Turing definition of computable functions is not needed from a constructive point of view. We give in this paper a constructive theory of ordinals that is similar to Martin-Löf's theory, but based only on the two relations "x \leq y" and "x < y", i.e. without considering sequents whose intuitive meaning is a classical disjunction. In our setting, the operation "supremum of ordinals" plays an important rôle through its interactions with the relations "x \leq y" and "x < y". This allows us to approach as much as we may the notion of linear order when the property "\alpha \leq \beta or \beta \leq \alpha" is provable only within classical logic. Our aim is to give a formal definition corresponding to intuition, and to prove that our constructive ordinals satisfy constructively all desirable properties.
Fichier principal
Vignette du fichier
ConstructiveOrdinals.pdf (342.5 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03522215 , version 1 (11-01-2022)

Identifiants

Citer

Thierry Coquand, Henri Lombardi, Stefan Neuwirth. Constructive theory of ordinals. Marco Benini; Olaf Beyersdorff; Michael Rathjen; Peter Schuster. Mathematics for Computation - M4C, World Scientific, In press. ⟨hal-03522215⟩
39 Consultations
141 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More