K-trivial set

Known as: K-trivial sets

In mathematics, a set of natural numbers is called a K-trivial set if its initial segments viewed as binary strings are easy to describe: the prefix…

Papers overview

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2017

2017

In algorithmic randomness, the class of K-trivial sets has proved itself to be remarkable, due to its numerous different…

2017

Martin-Löf (ML)-reducibility compares K-trivial sets by examining the Martin-Löf random sequences that compute them. We show that…

2016

We study the sets that are computable from both halves of some (Martin-Löf) random sequence, which we call 1{2-bases. We show…

2014

Abstract The K-trivial sets form an ideal in the Turing degrees, which is generated by its computably enumerable (c.e.) members…

2014

We prove that superhigh sets can be jump traceable, answering a question of Cole and Simpson. On the other hand, we show that…

2013

We present a notion of forcing that can be used, in conjunction with other results, to show that there is a Martin-L\"of random…

2012

Monotone complexity, Km, is a variant of Kolmogorov complexity that was introduced independently by Levin and Schnorr. The…

2010

In this chapter, we introduce an important class of “randomnesstheoretically weak” sets, the K-trivial sets. As we will see, this…

1985