Forcing Idealized
Seiten
2008
Cambridge University Press (Verlag)
978-0-521-87426-7 (ISBN)
Cambridge University Press (Verlag)
978-0-521-87426-7 (ISBN)
Though descriptive set theory and definable proper forcing are two areas of set theory that developed quite independently of each other, there are deep connections to be made between them. This monograph explores these links, and many examples of forcing notions appear, from measure theory, dynamical systems, and other fields.
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.
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.
| Erscheint lt. Verlag | 7.2.2008 |
|---|---|
| Reihe/Serie | Cambridge Tracts in Mathematics |
| Zusatzinfo | Worked examples or Exercises; 3 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 160 x 234 mm |
| Gewicht | 638 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| ISBN-10 | 0-521-87426-2 / 0521874262 |
| ISBN-13 | 978-0-521-87426-7 / 9780521874267 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Buch | Hardcover (2023)
Hanser, Carl (Verlag)
CHF 41,95
