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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:713256 |
| Date | January 2017 |
| Creators | Riley, James |
| Contributors | Truss, John ; Cooper, S.Barry ; Lewis-Pye, Andrew |
| Publisher | University of Leeds |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://etheses.whiterose.ac.uk/17198/ |
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