TWO MORE CHARACTERIZATIONS OF K-TRIVIALITY

Abstract : We give two new characterizations of K-triviality. We show that if for all Y such that Ω is Y-random, Ω is (Y ⊕ A)-random, then A is K-trivial. The other direction was proved by Stephan and Yu, giving us the first titular characterization of K-triviality and answering a question of Yu. We also prove that if A is K-trivial, then for all Y such that Ω is Y-random, (Y ⊕ A) ≡ LR Y. This answers a question of Merkle. The other direction is immediate, so we have the second characterization of K-triviality. The proof of the first characterization uses a new cupping result. We prove that if A is not LR below B, then for every set X there is a B-random set Y such that X is computable from Y ⊕ A.
Type de document :
Article dans une revue
Notre Dame Journal of Formal Logic, University of Notre Dame, 2016
Liste complète des métadonnées

Littérature citée [16 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01397290
Contributeur : Benoit Monin <>
Soumis le : mardi 15 novembre 2016 - 16:12:16
Dernière modification le : jeudi 17 novembre 2016 - 01:04:34
Document(s) archivé(s) le : jeudi 16 mars 2017 - 13:39:38

Fichier

preserving.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01397290, version 1

Collections

Citation

Noam Greenberg, Joseph Miller, Benoit Monin, Daniel Turetsky. TWO MORE CHARACTERIZATIONS OF K-TRIVIALITY. Notre Dame Journal of Formal Logic, University of Notre Dame, 2016. 〈hal-01397290〉

Partager

Métriques

Consultations de la notice

111

Téléchargements de fichiers

91