HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

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.
Document type :
Journal articles
Complete list of metadata

Cited literature [16 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01397290
Contributor : Benoit Monin Connect in order to contact the contributor
Submitted on : Tuesday, November 15, 2016 - 4:12:16 PM
Last modification on : Wednesday, November 3, 2021 - 6:49:43 AM
Long-term archiving on: : Thursday, March 16, 2017 - 1:39:38 PM

File

preserving.pdf
Files produced by the author(s)

Identifiers

  • 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⟩

Share

Metrics

Record views

119

Files downloads

103