Set Theory Exploring Independence and Truth [Paperback]

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.

A book like this is not only useful, it is necessary for set theory. It contains great results, some of the most celebrated in set theory, it finally has a comprehensive exposition of many essential tools & this is the perfect book for someone who already is familiar with set theory, and wants to know more about this specific part. It is also a good introduction for somebody who comes from outside set theory, but is curious about it. (Vincenzo Dimonte, Studia Logica, Vol. 106, 2018)

This text is, in its own way, a remarkable accomplishment. While a Universitext, it somehow manages to pursue a steady path of exposition from the beginnings in the seminal work lÓ%