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2-tactics in the Choquet game, and the filter dichotomy

This thesis is comprised of two parts. The first part (Chapter 1) concerns a problem born from descriptive set theory, and is motivated by the desire to understand a particular topological game, in the presence of examples which exhibit interesting (arguably counterintuitive) behaviour. The work develops an understanding of the limits of this behaviour, and indicates where one might look for interesting examples. While set-theoretic techniques may appear in the analysis here, the focus is mostly topological. The second part (Chapter 2) is much more set-theoretic. The work there developed from an interest in characterising closed subsets of βω, and focuses on developing tools which are promising for generalising the current relative consistency proofs of a duality principle for closed subsets of βωω. Knowledge of forcing comparable to that contained in Kunen and Jech is assumed. The appendices contain results which are worthy of inclusion, and help provide additional perspective on the rest of the text. The results there are probably all already known, if not all recorded in the literature.

Identiferoai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:668708
Date January 2014
CreatorsLupton, Richard J.
ContributorsKnight, Robin; Koenigsmann, Jochen
PublisherUniversity of Oxford
Source SetsEthos UK
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
Sourcehttp://ora.ox.ac.uk/objects/uuid:51d95948-a823-4b84-bc6e-f3c23de5d9ae

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