Mini-Workshop: Feinstrukturtheorie und Innere Modelle

Abstract

The main aim of fine structure theory and inner model theory can be summarized as the construction of models which have a canonical inner structure (a fine structure), making it possible to analyze them in great detail, and which at the same time reflect important aspects of the surrounding mathematical universe, in that they satisfy certain strong axioms of infinity, or contain complicated sets of reals. Applications range from obtaining lower bounds on the consistency strength of all sorts of set theoretic principles in terms of large cardinals, to proving the consistency of certain combinatorial properties, their compatibility with strong axioms of infinity, or outright proving results in descriptive set theory (for which no proofs avoiding fine structure and inner models are in sight). Fine structure theory and inner model theory has become a sophisticated and powerful apparatus which yields results that are among the deepest in set theory.