Set Theory

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.