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.
Papildus informācija
This book presents the theory of proper forcing and its relatives from the beginning. No prior knowledge of forcing is required.
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. -properness and
not adding reals;
6. Preservation of additional properties, and applications;
7. Axioms and their application;
8. -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 1 is not
collapsed;
16. Large ideals on 1 from smaller cardinals;
17. Forcing axioms;
18. More on proper forcing; Appendix. On weak diamonds and the power of ext;
References; More references.
Saharon Shelah works in the Institute of Mathematics at the Hebrew University of Jerusalem and in the Department of Mathematics at Rutgers University, New Jersey.
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