Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 60, Number 1 (2019), 119-138.
Levels of Uniformity
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.
Notre Dame J. Formal Logic, Volume 60, Number 1 (2019), 119-138.
Received: 1 November 2015
Accepted: 30 November 2016
First available in Project Euclid: 18 January 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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)
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