White Rose University Consortium logo
University of Leeds logo University of Sheffield logo York University logo

Automorphisms and linearisations of computable orderings

Lee, Kyung Il (2011) Automorphisms and linearisations of computable orderings. PhD thesis, University of Leeds.

[img]
Preview
Text
Lee_K_Mathematics_PhD_2009.pdf
Available under License Creative Commons Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales.

Download (534Kb)

Abstract

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.

Item Type: Thesis (PhD)
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds)
Depositing User: Repository Administrator
Date Deposited: 27 Feb 2012 11:01
Last Modified: 07 Mar 2014 11:24
URI: http://etheses.whiterose.ac.uk/id/eprint/2166

Actions (repository staff only: login required)