The Ultrapower Axiom / / Gabriel Goldberg.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2022 Part 1
• VerfasserIn: Goldberg, Gabriel,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2022]; ©2022
• Year of Publication: 2022
• Language: English
• Series: De Gruyter Series in Logic and Its Applications , 10
• Physical Description: 1 online resource (X, 326 p.)
• Other title: Frontmatter --; 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110719734; 9783110766820; 9783110993899; 9783110994810; 9783110993868; 9783110770445
• ISSN: 1438-1893
• DOI: 10.1515/9783110719734
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Gabriel Goldberg.

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.