Proper and Improper Forcing

ISBN-13: 9781107168367 / Angielski / Twarda / 2017 / 1066 str.

Saharon Shelah

Opis

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.

Spis treści

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 א1 is not collapsed; 16. Large ideals on א1 from smaller cardinals; 17. Forcing axioms; 18. More on proper forcing; Appendix. On weak diamonds and the power of ext; References; More references.