Set Theory: Exploring Independence And Truth (universitext)
by Ralf Schindler /
2014 / English / PDF
1.9 MB Download
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
Jensens 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.
