Perspectives in Logic

Proper and Improper Forcing

Saharon Shelah

Perspectives in Mathematical Logic, Volume 5
Berlin: Springer-Verlag, 1998. 2nd
1020 pp.

Subjects:

03E05 (primary)
03E35 (primary)
03E45 (primary)
03E50 (primary)
Permanent link to this monograph: http://projecteuclid.org/euclid.pl/1235419814
Mathmatical Reviews number (MathSciNet): MR1623206
ISBN:3-540-51700-6

Copyright © 1998, Association for Symbolic Logic.

Miscellaneous Frontmatter

Introduction

xv-xlvii

Chapter I: Forcing, Basic Facts

1-49

Chapter II: Iteration of Forcing

50-88

Chapter III: Proper Forcing

89-143

Chapter IV: On Oracle-c.c.,the Lifting Problem of the Measure Algebra, and "$\mathcal{P}(\omega)$/finite Has No Non-trivial Automorphism"

144-193

Chapter V: $\alpha$-Properness and Not Adding Reals

194-246

Chapter VI: Preservation of Additional Properties, and Applications

247-371

Chapter VII: Axioms and Their Application

372-402

Chapter VIII: $\kappa$-pic and Not Adding Reals

403-435

Chapter IX: Souslin Hypothesis Does Not Imply "Every Aronszajn Tree Is Special"

436-466

Chapter X: On Semi-Proper Forcing

467-531

Chapter XI: Changing Cofinalities; Equi-Consistency Results

532-588

Chapter XII: Improper Forcing

589-603

Chapter XIII: Large Ideals on $\omega_1$

604-678

Chapter XIV: Iterated Forcing with Uncountable Support

679-731

Chapter XV: A More General Iterable Condition Ensuring $\aleph_1$ Is Not Collapsed

732-777

Chapter XVI: Large Ideals on $\aleph_1$ from Smaller Cardinals

778-802

Chapter XVII: Forcing Axioms

803-853

Chapter XVIII: More on Proper Forcing

854-939

Appendix: On Weak Diamonds and the Power of Ext

940-995

References

997-1020

Miscellaneous Backmatter