Euclidean Functions of Computable Euclidean Domains
Rodney G. Downey, Asher M. Kach · Notre Dame Journal of Formal Logic · 2011
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.