Extensions of the Axiom of Blackwell Determinacy
Title | Extensions of the Axiom of Blackwell Determinacy PDF eBook |
Author | Benedikt Löwe |
Publisher | |
Pages | 9 |
Release | 2005 |
Genre | |
ISBN |
The Axiom of Real Blackwell Determinacy
Title | The Axiom of Real Blackwell Determinacy PDF eBook |
Author | Daisuke Ikegami |
Publisher | |
Pages | 15 |
Release | 2009 |
Genre | |
ISBN |
A Note on Pure Variations of Axioms of Blackwell Determinacy
Title | A Note on Pure Variations of Axioms of Blackwell Determinacy PDF eBook |
Author | Benedikt Löwe |
Publisher | |
Pages | 7 |
Release | 2004 |
Genre | |
ISBN |
Extensions of the Axiom of Determinacy
Title | Extensions of the Axiom of Determinacy PDF eBook |
Author | Paul B. Larson |
Publisher | American Mathematical Society |
Pages | 182 |
Release | 2023-10-19 |
Genre | Mathematics |
ISBN | 1470472104 |
This is an expository account of work on strong forms of the Axiom of Determinacy (AD) by a group of set theorists in Southern California, in particular by W. Hugh Woodin. The first half of the book reviews necessary background material, including the Moschovakis Coding Lemma, the existence of strong partition cardinals, and the analysis of pointclasses in models of determinacy. The second half of the book introduces Woodin's axiom system $mathrm{AD}^{+}$ and presents his initial analysis of these axioms. These results include the consistency of $mathrm{AD}^{+}$ from the consistency of AD, and its local character and initial motivation. Proofs are given of fundamental results by Woodin, Martin, and Becker on the relationships among AD, $mathrm{AD}^{+}$, the Axiom of Real Determinacy, and the Suslin property. Many of these results are proved in print here for the first time. The book briefly discusses later work and fundamental questions which remain open. The study of models of $mathrm{AD}^{+}$ is an active area of contemporary research in set theory. The presentation is aimed at readers with a background in basic set theory, including forcing and ultrapowers. Some familiarity with classical results on regularity properties for sets of reals under AD is also expected.
The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal
Title | The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal PDF eBook |
Author | W. Hugh Woodin |
Publisher | Walter de Gruyter |
Pages | 944 |
Release | 2013-02-01 |
Genre | Mathematics |
ISBN | 3110804735 |
The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.
Sets and Extensions in the Twentieth Century
Title | Sets and Extensions in the Twentieth Century PDF eBook |
Author | |
Publisher | Elsevier |
Pages | 878 |
Release | 2012-01-24 |
Genre | Mathematics |
ISBN | 0080930662 |
Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration - Serves as a singular contribution to the intellectual history of the 20th century - Contains the latest scholarly discoveries and interpretative insights
The Bulletin of Symbolic Logic
Title | The Bulletin of Symbolic Logic PDF eBook |
Author | |
Publisher | |
Pages | 132 |
Release | 2009 |
Genre | Logic, Symbolic and mathematical |
ISBN |