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Structural properties of the local Turing degrees

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

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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

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