The Ultrapower Axiom

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.