Set Theory: Exploring Independence and Truth (Universitext)

This textbook gives an introduction to axiomatic set theory and examines the prominent questions that are relevant in current research in a manner that is accessible to students. Its main theme is the interplay of large cardinals, inner models, forcing and descriptive set theory.
The following topics are covered:

. Forcing and constructability
. The Solovay-Shelah Theorem i.e. the equiconsistency of 'every set of reals is Lebesgue measurable' with one inaccessible cardinal
. Fine structure theory and a modern approach to sharps
. Jensen's Covering Lemma
. The equivalence of analytic determinacy with sharps
. The theory of extenders and iteration trees
. A proof of projective determinacy from Woodin cardinals.

Set Theory requires only a basic knowledge of mathematical logic and will be suitable for advanced students and researchers.