Open Access
2019 Levels of Uniformity
Rutger Kuyper
Notre Dame J. Formal Logic 60(1): 119-138 (2019). DOI: 10.1215/00294527-2018-0024


We introduce a hierarchy of degree structures between the Medvedev and Muchnik lattices which allow varying amounts of nonuniformity. We use these structures to introduce the notion of the uniformity of a Muchnik reduction, which expresses how uniform a reduction is. We study this notion for several well-known reductions from algorithmic randomness. Furthermore, since our new structures are Brouwer algebras, we study their propositional theories. Finally, we study if our new structures are elementarily equivalent to each other.


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Rutger Kuyper. "Levels of Uniformity." Notre Dame J. Formal Logic 60 (1) 119 - 138, 2019.


Received: 1 November 2015; Accepted: 30 November 2016; Published: 2019
First available in Project Euclid: 18 January 2019

zbMATH: 07060310
MathSciNet: MR3911108
Digital Object Identifier: 10.1215/00294527-2018-0024

Primary: 03D30 , 03D32
Secondary: 03B20 , 03G10

Keywords: algorithmic randomness , Medvedev degrees , Muchnik degrees

Rights: Copyright © 2019 University of Notre Dame

Vol.60 • No. 1 • 2019
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