Open Access
2011 Euclidean Functions of Computable Euclidean Domains
Rodney G. Downey, Asher M. Kach
Notre Dame J. Formal Logic 52(2): 163-172 (2011). DOI: 10.1215/00294527-1306172


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.


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Rodney G. Downey. Asher M. Kach. "Euclidean Functions of Computable Euclidean Domains." Notre Dame J. Formal Logic 52 (2) 163 - 172, 2011.


Published: 2011
First available in Project Euclid: 28 April 2011

zbMATH: 1260.03082
MathSciNet: MR2794649
Digital Object Identifier: 10.1215/00294527-1306172

Primary: 03D45
Secondary: 03B30

Keywords: Euclidean domain , Euclidean function

Rights: Copyright © 2011 University of Notre Dame

Vol.52 • No. 2 • 2011
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