Ralf Schindler: Exploring Independence and Truth, Springer 2014
” 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.”