$\Pi^0_4$ conservation of Ramsey's theorem for pairs - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

$\Pi^0_4$ conservation of Ramsey's theorem for pairs

Résumé

In this article, we prove that Ramsey's theorem for pairs and two colors is a $\forall \Pi^0_4$ conservative extension of~$\mathsf{RCA}_0 + \mathsf{B}\Sigma^0_2$, where a $\forall \Pi^0_4$ formula consists of a universal quantifier over sets followed by a $\Pi^0_4$ formula. The proof is an improvement of a result by Patey and Yokoyama and a step towards the resolution of the longstanding question of the first-order part of Ramsey's theorem for pairs.
Fichier principal
Vignette du fichier
pi04-conservation-rt22.pdf (484.64 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04563930 , version 1 (30-04-2024)

Identifiants

  • HAL Id : hal-04563930 , version 1

Citer

Quentin Le Houérou, Ludovic Levy Patey, Keita Yokoyama. $\Pi^0_4$ conservation of Ramsey's theorem for pairs. 2024. ⟨hal-04563930⟩
10 Consultations
4 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More