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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.§
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