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.
General
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