Set Theory

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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.