## Notre Dame Journal of Formal Logic

### Levels of Uniformity

Rutger Kuyper

#### Abstract

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.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 60, Number 1 (2019), 119-138.

Dates
Accepted: 30 November 2016
First available in Project Euclid: 18 January 2019

https://projecteuclid.org/euclid.ndjfl/1547802297

Digital Object Identifier
doi:10.1215/00294527-2018-0024

Mathematical Reviews number (MathSciNet)
MR3911108

Zentralblatt MATH identifier
07060310

#### Citation

Kuyper, Rutger. Levels of Uniformity. Notre Dame J. Formal Logic 60 (2019), no. 1, 119--138. doi:10.1215/00294527-2018-0024. https://projecteuclid.org/euclid.ndjfl/1547802297

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