The Ultrapower Axiom

Gabriel Goldberg

Published by De Gruyter 2022

The Ultrapower Axiom

Gabriel Goldberg

Volume 10 in the series De Gruyter Series in Logic and Its Applications

https://doi.org/10.1515/9783110719734

Overview
Contents

About this book

The book is about strong axioms of infi nity in set theory (also known as large cardinal axioms), and the ongoing search for natural models of these axioms. Assuming the Ultrapower Axiom, a combinatorial principle conjectured to hold in all such natural models, we solve various classical problems in set theory (for example, the Generalized Continuum Hypothesis) and uncover a theory of large cardinals that is much clearer than the one that can be developed using only the standard axioms.

Developed and expanded from a prize winning thesis in logic.
First treatment of the Ultra Power Axiom clarifying gaps in the understanding of large cardinal hierarchy.
Clearly written proofs accessible to all readers.

Author / Editor information

Gabriel Goldberg, UC Berkeley, Berkeley, USA.

Topics

Frontmatter Publicly Available Download PDF	I
Acknowledgments Publicly Available Download PDF	V
Contents Publicly Available Download PDF	VII
1 Introduction Requires Authentication Unlicensed Licensed Download PDF	1
2 The linearity of the Mitchell order Requires Authentication Unlicensed Licensed Download PDF	7
3 The Ketonen order Requires Authentication Unlicensed Licensed Download PDF	35
4 The generalized Mitchell order Requires Authentication Unlicensed Licensed Download PDF	71
5 The Rudin–Frolík order Requires Authentication Unlicensed Licensed Download PDF	117
6 V = HOD and GCH from UA Requires Authentication Unlicensed Licensed Download PDF	163
7 The least supercompact cardinal Requires Authentication Unlicensed Licensed Download PDF	183
8 Higher supercompactness Requires Authentication Unlicensed Licensed Download PDF	249
9 Open questions Requires Authentication Unlicensed Licensed Download PDF	307
Bibliography Requires Authentication Unlicensed Licensed Download PDF	319
Index Requires Authentication Unlicensed Licensed Download PDF	321

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers and Graduate Students.
Pages
- Front matter: 10
- Main content: 326
Illustrations
- Illustrations: 29
Keywords: Logik; Analysis

eBook

Published: April 4, 2022
ISBN: 9783110719734

Hardcover

Published: April 18, 2022
ISBN: 9783110719697