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 prefixâ€¦Â (More)

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2016

2016

Computing from Projections of Random Points: a Dense Hierarchy of Subideals of the K-trivial Degrees

We study the sets that are computable from both halves of some (Martin-LÃ¶f) random sequence, which we call 1{2-bases. We showâ€¦Â (More)

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2015

2015

We introduce Oberwolfach randomness, a notion within Demuthâ€™s framework of statistical tests with moving components; here theâ€¦Â (More)

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Review

2015

Review

2015

- Laurent Bienvenu, Alexander Shen
- Fields of Logic and Computation II
- 2015

A remarkable achievement in algorithmic randomness and algorithmic information theory was the discovery of the notions of Kâ€¦Â (More)

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2014

2014

- George Barmpalias, Rodney G. Downey
- J. Symb. Log.
- 2014

The K-trivial sets form an ideal in the Turing degrees, which is generated by its computably enumerable (c.e.) members and has anâ€¦Â (More)

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2013

2013

- Noam Greenberg
- CiE
- 2013

Every K-trivial set is computable from an incomplete Martin-LÃ¶f random set, i.e., a Martin-LÃ¶f random set that does not computeâ€¦Â (More)

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2012

2012

- Daniel Turetsky
- Inf. Process. Lett.
- 2012

We construct a K-trivial c.e. set which is not jump traceable at any order in o(log x).Â

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2010

2010

In [RS07, RS08], Reimann and Slaman raise the question â€œFor which infinite binary sequences X do there exist continuousâ€¦Â (More)

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2006

2006

Let R be a notion of algorithmic randomness for individual subsets of N. We say B is a base for R randomness if there is a Z >T Bâ€¦Â (More)

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2005

2005

An analog of ML-randomness in the effective descriptive set theory setting is studied, where the r.e. objects are replaced byâ€¦Â (More)

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2005

2005

- AndrÃ© Nies, AndrÃ© Nies
- 2005

We investigate combinatorial lowness properties of sets of natural numbers (reals). The real A is super-low if Aâ€² â‰¤tt âˆ…â€², and Aâ€¦Â (More)

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