The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal

2. rev. Auflage 2010
ISBN: 978-3-11-019702-0
Verlag: De Gruyter

Buch, Englisch, Band 1, 852 Seiten, Format (B × H): 175 mm x 246 mm, Gewicht: 1609 g

Reihe: De Gruyter Series in Logic and Its Applications

The starting point for this monograph is the previously unknown connection between the Continuum Hypothesis and the saturation of the non-stationary ideal on ?; and the principle result of this monograph is the identification of a canonical model in which the Continuum Hypothesis is false. This is the first example of such a model and moreover the model can be characterized in terms of maximality principles concerning the universal-existential theory of all sets of countable ordinals. This model is arguably the long sought goal of the study of forcing axioms and iterated forcing but is obtained by completely different methods, for example no theory of iterated forcing whatsoever is required. The construction of the model reveals a powerful technique for obtaining independence results regarding the combinatorics of the continuum, yielding a number of results which have yet to be obtained by any other method.

This monograph is directed to researchers and advanced graduate students in Set Theory. The second edition is updated to take into account some of the developments in the decade since the first edition appeared, this includes a revised discussion of O-logic and related matters.

Zielgruppe

Academic and professional

Autoren/Hrsg.

Woodin, W. Hugh

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik

Inhaltsverzeichnis

Frontmatter
Contents
1 Introduction
2 Preliminaries
3 The nonstationary ideal
4 The Pmax-extension
5 Applications
6 Pmax variations
7 Conditional variations
8 ? principles for ? 1

9 Extensions of L(G, R)
10 Further results
11 Questions
Backmatter

Über Autor(innen)

Woodin, W. Hugh
W. Hugh Woodin, University of California, Berkeley, USA.