Automorphisms and linearisations of computable orderings
Kyung Il Lee · White Rose eTheses Online (University of Leeds, The University of Sheffield, University of York) · 2011
In this thesis, we study computable content of existing classical theorems on linearisations of partial orderings and automorphisms of linear orderings, and provide computational refinements in terms of the Ershov hierarchy. In Chapter 2, we examine questions as to the constructiveness of linearisations obtained in terms of the Ershov hierarchy, while respecting particular constraints. The main result here entails a proof that every computably well-founded computable partial ordering has a computably well-founded ω-c.e. linear extension. In Chapter 3, we examine questions as to how less constructive rigidities of certain order types break down within the context of the Ershov hierarchy, and introduce uniform Δ02 classes as likely candidates in the case of order types 2.η and ω + ς.