We construct two computable topologically conjugate functions for which no
conjugacy is computable, or even hyperarithmetic, resolving an open question of
Kennedy and Stockman.Comment: 9 pages. v2 adds a note on folklor

Westrick, Linda Brown

English

arXiv

Abstract. We construct two computable topologically conjugate functions for which no conjugacy is computable, or even hyperarithmetic, resolving an open question of Kennedy and Stockman [Pea07]. Author’s Note After this was written up I learned that most of the ideas below are effectiviza-tions of folk theorems which were known to descriptive set theorists. Hjorth has given a nice account of these in section 4.2 of his book Classification and orbit equivalence relations [Hjo00]. The non-logician who wants to understand the basic idea could still use Sections 2 and 3 as an accessible expository construction of a pair of computable topologically conjugate functions with no computable conjugacy. If one already has some familiarity with computable analysis and is interested in the hyperarithmetic aspect, I would recommend reading Hjorth’s book instead, because the presentation there suggests a cleaner way to encode linear orders into homeomorphisms

Topological conjugations are not constructable

Abstract

Similar works

Full text

Available Versions

CiteSeerX