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

Structural properties of the local Turing degrees

Riley, James (2017) Structural properties of the local Turing degrees. PhD thesis, University of Leeds.

[img]
Preview
Text
James.Riley.Thesis.pdf - Final eThesis - complete (pdf)
Available under License Creative Commons Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales.

Download (348Kb) | Preview

Abstract

In this thesis we look at some properties of the local Turing Degrees, as a partial order. We first give discussion of the Turing Degrees and certain historical results, some translated into a form resembling the constructions we look at later. Chapter 1 gives a introduction to the Turing Degrees, Chapter 2 introduces the Local Degrees. In Chapter 3 we look at minimal Turing Degrees, modifying some historical results to use a priority tree, which we use in chapter 4 to prove the new result that every c.e. degree has the (minimal) meet property. Chapter 5 uses similar methods to establish existence of a high 2 degree that does not have the meet property.

Item Type: Thesis (PhD)
Keywords: Turing degrees
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds)
Identification Number/EthosID: uk.bl.ethos.713256
Depositing User: Mr James Riley
Date Deposited: 16 May 2017 12:55
Last Modified: 25 Jul 2018 09:54
URI: http://etheses.whiterose.ac.uk/id/eprint/17198

You do not need to contact us to get a copy of this thesis. Please use the 'Download' link(s) above to get a copy.
You can contact us about this thesis. If you need to make a general enquiry, please see the Contact us page.

Actions (repository staff only: login required)