The isometry degree of a computable copy of ℓ^p

2016/05/02 by Timothy H. McNicholl, McNicholl, Timothy H., D. M. Stull +1
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #Advanced Topology and Set Theory #Cellular Automata and Applications

paper · pdf · doi:10.48550/arxiv.1605.00641

Abstract

When p is a computable real so that p ≥ 1, the isometry degree of a computable copy B of ℓ^p is defined to be the least powerful Turing degree that computes a linear isometry of ℓ^p onto B. We show that this degree always exists and that when p ≠ 2 these degrees are precisely the c.e. degrees.

Related

• Computable copies of ℓ^p
• Turing degrees of isomorphism types of geometric objects
• Degrees of and lowness for isometric isomorphism
• Isomorphism Spectra and Computably Composite Structures
• Relative to any non-arithmetic set