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Proper and Improper Forcing

2nd Edition

$216.00 (C)

Part of Perspectives in Logic

  • Date Published: May 2017
  • availability: Available
  • format: Hardback
  • isbn: 9781107168367

$ 216.00 (C)

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About the Authors
  • 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.

    • A revised and expanded edition of a previous title in this series, Proper Forcing
    • Presents both particular consistency results and methods which can be used for such independence results
    • No prior knowledge of forcing is assumed
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    Product details

    • Edition: 2nd Edition
    • Date Published: May 2017
    • format: Hardback
    • isbn: 9781107168367
    • length: 1066 pages
    • dimensions: 240 x 158 x 62 mm
    • weight: 1.7kg
    • availability: Available
  • Table of Contents

    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
    More references.

  • Author

    Saharon Shelah, Hebrew University of Jerusalem
    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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