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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

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

Lupton, Richard J. January 2014 (has links)
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.
2

Higher gap morasses

Cárdenas, Franqui 26 August 2005 (has links)
Velleman beweist die Konsistenz der Existenz vereinfachte Gap 2 Moraste (ein Begriff gleichwertig zu den ursprünglichen Morasten, geschafft von Jensen). Wir haben einen noch einfachen Begriff des vereinfachten Morastes in der Dissertation vorgeschlagen, Details aufgefüllt und wesentlich auch einen verschiedenen Beweis des Satzes erfunden und zwar in beide Stufe des Forcingverfahrens. Wir benötigen auch keine Squarefunktionereihenfolge (die ganz Kohärenzvoraussetzung fehlt aber ist linear und konfinal) sondern ein ``erratendes'' Verfahren für Sequenze, das nicht fest ist und nicht die ganze Kohärenzbedigung erfüllt wie bei Velleman. Wir hoffen, wir haben so eingelegt die Basis für einen zukunftigen Beweis des allgemeines Falls n in ZFC. / Velleman proved the consistency of the existence of simplified gap 2 morasses (equivalent to the concrete morasses defined by Jensen) using a two stage forcing. We give an essentially different proof of the same result and fill up some details from Velleman's paper which were not clear or imcomplete. In fact the proof uses a simpler definition of simplified gap 2 morasses. We have also eliminated the use of square-like sequences in the second stage, employing a ``guessing'' procedure for sequences which are not fixed and do not satisfy full coherence requirement. With these steps we hope to have laid the foundation for a future proof of gap n morasses in ZFC.

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