SET THEORY - EXPLORING INDEPENDENCE AND TRUTH

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.