Fine Structure and Class Forcing

✍ Scribed by Sy D. Friedman

• Publisher: De Gruyter
• Year: 2000
• Tongue: English
• Leaves: 232
• Series: De Gruyter Series in Logic and Its Applications; 3
• Edition: Reprint 2011
• Category: Library

✦ Synopsis

"The author has not been loath to publish his ongoing work nor to present it in systematic lectures and courses, and the volume under review could be regarded as a compendium of work that has already appeared in print. However, both in its integration of the work and the simplifications afforded by steady research in the subject, the book is pleasingly accessible, satisfying self-contained, and magisterial in presentation. […] This volume is enticing in its elegance and simplicity at first and inveigles the reader to get involved in some of its later complexities." Mathematical Reviews

✦ Table of Contents

Preface
1 The Σ* Approach to the Fine Structure of L
1.1 The J-Hierarchy
1.2 Fine Structure Theory
1.3 Morasses
2 Forcing
2.1 Set Forcing
2.2 Class Forcing
2.3 Examples
3 Construction of Generic Classes
3.1 Rigidity
3.2 Relevant Forcing
4 The Coding Theorem
4.1 Three Questions of Solovay
4.2 The Coding Theorem without 0#
4.3 The Coding Theorem in the General Case
4.4 Large Cardinal Preservation and Relevance
5 The Genericity Problem
5.1 Jensen’s Example and a New Conjecture
5.2 Perturbing the Indiscernibles
5.3 Generic Saturation
6 The π12-Singleton Problem
6.1 An Absolute Singleton
6.2 David’s Trick
6.3 Other Applications
7 The Admissibility Spectrum Problem
7.1 Killing Admissibles
7.2 Strong Coding
7.3 Other Spectra
8 Further Applications of Class Forcing
8.1 Δ1-Coding
8.2 Iterated Class Forcing
8.3 Minimal Coding
8.4 Further Applications to Descriptive Set Theory
Some Open Problems
References
Index