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Provides a fairly self-contained introduction to set theory, in particular to the theory of inner models and forcing
Presents essential aspects of set theory which are required in understanding modern developments of descriptive inner model theory
Includes proofs of landmark results at the interface of the theory of large cardinals and descriptive 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.
Content Level »Graduate
Keywords »Constructibility - Extenders - Fine Structure Theory - Forcing - Iteration Trees - Jensen’s Covering Lemma - Large Cardinals - Solovay’s Model - The Martin-Harrington Theorem - The Martin-Steel Theorem - The Solovay-Shelah Theorem