Riley, James (2017) Structural properties of the local Turing degrees. PhD thesis, University of Leeds.
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.
Metadata
Supervisors: | Truss, John and Cooper, S Barry and Lewis-Pye, Andrew |
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Keywords: | Turing degrees |
Awarding institution: | University of Leeds |
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 |
Open Archives Initiative ID (OAI ID): | oai:etheses.whiterose.ac.uk:17198 |
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