Proper and Improper Forcing (Perspectives in Logic)

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Saharon ShelahCambridge University PressEdition: 2, 3/23/2017EAN 9781107168367, ISBN10: 1107168368Hardcover, 1066 pages, 23.4 x 15.6 x 6.2 cmLanguage: EnglishSince 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.Introduction1. Forcing, basic facts2. Iteration of forcing3. Proper forcing4. 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 reals6. Preservation of additional properties, and applications7. Axioms and their application8. κ-pic and not adding reals9. Souslin hypothesis does not imply 'every Aronszajn tree is special'10. On semi-proper forcing11. Changing confinalitiesequi-consistency results12. Improper forcing13. Large ideals on w114. Iterated forcing with uncountable support15. A more general iterable condition ensuring א1 is not collapsed16. Large ideals on א1 from smaller cardinals17. Forcing axioms18. More on proper forcingAppendix. On weak diamonds and the power of extReferencesMore references. Show more