Naive set theory.- Axiomatic set theory.- Ordinals.- Cardinals.- Constructability.- Forcing.- Descriptive set theory.- Solovay's model.- The Raisonnier filter.- Measurable cardinals.- 0# and Jensen's Covering Lemma.- Analytic and full determinacy.- Projective determinacy.
Ralf Schindler teaches at Universitat Munster and is an expert in the field of set theory.Ralf Schindler works mostly in the area of descriptive inner model theory. His results are on the construction of inner models and core models, on coding over core models and on applications of inner model theory to descriptive set theory and combinatorics. He isolated the concept of a "remarkable" cardinal.
"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 of Cantor through to Jensen's covering Lemma and the Martin-Steel Theorem on Projective Determinacy. ... this text could well be considered an informative one even for the set theorist." (A. Kanamori, Mathematical Reviews, June, 2015)