Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 59, Number 2 (2018), 189-195.
Two More Characterizations of K-Triviality
We give two new characterizations of -triviality. We show that if for all such that is -random, is -random, then is -trivial. The other direction was proved by Stephan and Yu, giving us the first titular characterization of -triviality and answering a question of Yu. We also prove that if is -trivial, then for all such that is -random, . This answers a question of Merkle and Yu. The other direction is immediate, so we have the second characterization of -triviality.
The proof of the first characterization uses a new cupping result. We prove that if , then for every set there is a -random set such that is computable from .
Notre Dame J. Formal Logic, Volume 59, Number 2 (2018), 189-195.
Received: 22 March 2015
Accepted: 9 May 2015
First available in Project Euclid: 2 February 2018
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Greenberg, Noam; Miller, Joseph S.; Monin, Benoit; Turetsky, Daniel. Two More Characterizations of K -Triviality. Notre Dame J. Formal Logic 59 (2018), no. 2, 189--195. doi:10.1215/00294527-2017-0021. https://projecteuclid.org/euclid.ndjfl/1517540521