Notre Dame Journal of Formal Logic

Levels of Uniformity

Rutger Kuyper

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

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1547802297

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

Mathematical Reviews number (MathSciNet)
MR3911108

Zentralblatt MATH identifier
07060310

Subjects
Primary: 03D30: Other degrees and reducibilities 03D32: Algorithmic randomness and dimension [See also 68Q30]
Secondary: 03G10: Lattices and related structures [See also 06Bxx] 03B20: Subsystems of classical logic (including intuitionistic logic)

Keywords
Medvedev degrees Muchnik degrees algorithmic randomness

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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