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 researcher.