Forcing Idealized

Monograph exploring the connections that forcing makes with descriptive set theory and other areas of mathematics.

Jindrich Zapletal (Author)

9780521874267, Cambridge University Press

Hardback, published 7 February 2008

320 pages, 3 b/w illus. 26 exercises
23.4 x 16 x 2.1 cm, 0.638 kg

Descriptive set theory and definable proper forcing are two areas of set theory that developed quite independently of each other. This monograph unites them and explores the connections between them. Forcing is presented in terms of quotient algebras of various natural sigma-ideals on Polish spaces, and forcing properties in terms of Fubini-style properties or in terms of determined infinite games on Boolean algebras. Many examples of forcing notions appear, some newly isolated from measure theory, dynamical systems, and other fields. The descriptive set theoretic analysis of operations on forcings opens the door to applications of the theory: absoluteness theorems for certain classical forcing extensions, duality theorems, and preservation theorems for the countable support iteration. Containing original research, this text highlights the connections that forcing makes with other areas of mathematics, and is essential reading for academic researchers and graduate students in set theory, abstract analysis and measure theory.

1. Introduction
2. Basics
3. Properties
4. Examples
5. Operations
6. Applications
7. Questions
Bibliography
Index.

Subject Areas: Calculus & mathematical analysis [PBK], Algebra [PBF], Set theory [PBCH], Mathematical foundations [PBC]