This thesis concerns the study of the density of rational and algebraic points in the transcendental part of sets that are definable in o-minimal structures. An o-minimal version of a reparametrisation result of Yosef Yomdin is proved, Yomdin's result being the prototype of a result used to prove the Pila-Wilkie theorem. Subsequently we concentrate on a specific o-minimal structure, the real exponential field, and prove some partial results towards a conjecture of Wilkie concerning the particular paucity of rational points in sets definable in this structure. 2.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:555723 |
| Date | January 2012 |
| Creators | Butler, Lee A. |
| Publisher | University of Bristol |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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