Notre Dame Journal of Formal Logic

Euclidean Functions of Computable Euclidean Domains

Rodney G. Downey and Asher M. Kach

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Abstract

We study the complexity of (finitely-valued and transfinitely-valued) Euclidean functions for computable Euclidean domains. We examine both the complexity of the minimal Euclidean function and any Euclidean function. Additionally, we draw some conclusions about the proof-theoretical strength of minimal Euclidean functions in terms of reverse mathematics.

Article information

Source
Notre Dame J. Formal Logic Volume 52, Number 2 (2011), 163-172.

Dates
First available: 28 April 2011

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1303995712

Digital Object Identifier
doi:10.1215/00294527-1306172

Zentralblatt MATH identifier
05903676

Mathematical Reviews number (MathSciNet)
MR2794649

Subjects
Primary: 03D45: Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]
Secondary: 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35]

Keywords
Euclidean domain Euclidean function

Citation

Downey, Rodney G.; Kach, Asher M. Euclidean Functions of Computable Euclidean Domains. Notre Dame Journal of Formal Logic 52 (2011), no. 2, 163--172. doi:10.1215/00294527-1306172. http://projecteuclid.org/euclid.ndjfl/1303995712.


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