ABSTRACT

Presents Results from a Very Active Area of ResearchExploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive Set Theory presents an introduction to the basic concepts, methods, and results of this theory. It brings together techniques from various areas of mathem

chapter 1|36 pages

Preliminaries

chapter 2|32 pages

Polish Groups

chapter 3|26 pages

Polish Group Actions

chapter 4|18 pages

Finer Polish Topologies

part |2 pages

Part II: Theory of Equivalence Relations

chapter 5|16 pages

Borel Reducibility

chapter 6|24 pages

The Glimm–Effros Dichotomy

chapter 7|22 pages

Countable Borel Equivalence Relations

chapter 8|22 pages

Borel Equivalence Relations

chapter 9|22 pages

Analytic Equivalence Relations

chapter 10|22 pages

Turbulent Actions of Polish Groups

part |2 pages

Part III: Countable Model Theory

chapter 11|26 pages

Polish Topologies of Infinitary Logic

chapter 12|26 pages

The Scott Analysis

chapter 13|22 pages

Natural Classes of Countable Models

part |2 pages

Part IV: Applications to Classification Problems