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Iteration trees and genericity iterations

Iterationsbäume und Generizitätsiterationen
Authors: Wallner, Lena;

Iteration trees and genericity iterations

Abstract

Diese Arbeit ist eine sorgfältige und detailreiche Einführung in die Grundkonzepte der inneren Modelltheorie. Wir beginnen mit der Entwicklung der Konstruktion von Ultrapotenzen und Iterationsbäumen. Das erste Hauptresultat ist die (ω_1 +1)-Iterierbarkeit von schönen Iterationsbäumen und die schwache Iterierbarkeit. Anschließend diskutieren wir Generizitätsiterationen und nützliche Varianten davon. Diese werden im letzen Hauptresultat verwendet. Dort zeigen wir, dass L(R) ein Modell des Axioms der Determiniertheit ist.

This thesis is a careful and detailed introduction to the basic concepts of inner model theory. We start with developing the construction of ultrapowers and iteration trees. The first main result is the (ω_1 + 1)-iterability of nice iteration trees and weak iterability. We then discuss genericity iterations and some useful variants. They are used in the last main result which is that L(R) is a model of the Axiom of Determinacy.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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