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The Ultrapower Axiom

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The book is about strong axioms of infinity (also known as large cardinal axioms) in set theory, and the ongoing search for natural models of these axioms. Assuming the Ultrapower Axiom, we solve various classical problems in set theory (e.g., the Generalized Continuum Hypothesis) and develop a theory of large cardinals that is much clearer than the theory that can be developed using only the standard axioms.

Author(s): Gabriel Goldberg
Series: De Gruyter Series in Logic and Its Applications 10
Publisher: Walter de Gruyter GmbH & Co KG
Year: 2022

Language: English
Pages: 325

Acknowledgments
Contents
1 Introduction
2 The linearity of the Mitchell order
3 The Ketonen order
4 The generalized Mitchell order
5 The Rudin–Frolík order
6 V = HOD and GCH from UA
7 The least supercompact cardinal
8 Higher supercompactness
9 Open questions
Bibliography
Index