Set Theory

ebook Exploring Independence and Truth · Universitext

By Ralf Schindler

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.

  • Set Theory