Proper and Improper Forcing (Perspectives in Logic)
Cambridge University Press
Edition: 2, 3/23/2017
EAN 9781107168367, ISBN10: 1107168368
Hardcover, 1066 pages, 23.4 x 15.6 x 6.2 cm
Language: English
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the fifth publication in the Perspectives in Logic series, studies set-theoretic independence results (independence from the usual set-theoretic ZFC axioms), in particular for problems on the continuum. The author gives a complete presentation of the theory of proper forcing and its relatives, starting from the beginning and avoiding the metamathematical considerations. No prior knowledge of forcing is required. The book will enable a researcher interested in an independence result of the appropriate kind to have much of the work done for them, thereby allowing them to quote general results.
Introduction
1. Forcing, basic facts
2. Iteration of forcing
3. Proper forcing
4. On oracle-c.c., the lifting problem of the measure algebra, and 'P(w)/finite has no trivial automorphism'
5. α-properness and not adding reals
6. Preservation of additional properties, and applications
7. Axioms and their application
8. κ-pic and not adding reals
9. Souslin hypothesis does not imply 'every Aronszajn tree is special'
10. On semi-proper forcing
11. Changing confinalities
equi-consistency results
12. Improper forcing
13. Large ideals on w1
14. Iterated forcing with uncountable support
15. A more general iterable condition ensuring ×Â1 is not collapsed
16. Large ideals on ×Â1 from smaller cardinals
17. Forcing axioms
18. More on proper forcing
Appendix. On weak diamonds and the power of ext
References
More references.