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2018 Two More Characterizations of K-Triviality
Noam Greenberg, Joseph S. Miller, Benoit Monin, Daniel Turetsky
Notre Dame J. Formal Logic 59(2): 189-195 (2018). DOI: 10.1215/00294527-2017-0021


We give two new characterizations of K-triviality. We show that if for all Y such that Ω is Y-random, Ω is (YA)-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, (YA)LRY. This answers a question of Merkle and Yu. 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 ALRB, then for every set X there is a B-random set Y such that X is computable from YA.


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Noam Greenberg. Joseph S. Miller. Benoit Monin. Daniel Turetsky. "Two More Characterizations of K-Triviality." Notre Dame J. Formal Logic 59 (2) 189 - 195, 2018.


Received: 22 March 2015; Accepted: 9 May 2015; Published: 2018
First available in Project Euclid: 2 February 2018

zbMATH: 06870287
MathSciNet: MR3778306
Digital Object Identifier: 10.1215/00294527-2017-0021

Primary: 03D32
Secondary: 68Q30

Keywords: Kolmogorov complexity , K-triviality , Martin-Löf randomness

Rights: Copyright © 2018 University of Notre Dame


Vol.59 • No. 2 • 2018
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