Proper Forcing

1. Front Matter

   Pages I-XXIX

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2. Forcing, Basic Facts

   • Saharon Shelah

   Pages 1-38

3. Iteration of Forcing

   • Saharon Shelah

   Pages 39-72

4. Proper Forcing

   • Saharon Shelah

   Pages 73-113

5. On oracle-c.c. and “P(ω)/ finite has no non-trivial automorphism”

   • Saharon Shelah

   Pages 114-152

6. α- Properness and Not Adding Reals

   • Saharon Shelah

   Pages 153-194

7. P-Points and Preservation Theorems

   • Saharon Shelah

   Pages 195-232

8. The September Notes on Proper Forcing

   • Saharon Shelah

   Pages 233-257

9. The October Notes on Proper Forcing

   • Saharon Shelah

   Pages 258-277

10. Souslin Hypothesis Does Not Imply “Every Aronszajn Tree is Special”

    • Saharon Shelah

    Pages 278-303

11. On Semi-Proper Forcing

    • Saharon Shelah

    Pages 304-353

12. Changing Cofinalities; Equi-Consistency Results

    • Saharon Shelah

    Pages 354-393

13. Notes on Improper Forcing

    • Saharon Shelah

    Pages 394-409

14. Strong Covering Lemma and the G.C.H.

    • Saharon Shelah

    Pages 410-460

15. On Weak Diamonds and the Power of Ext

    • Saharon Shelah

    Pages 461-491

16. Back Matter

    Pages 492-498

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These notes can be viewed and used in several different ways, each has some justification, a collection of papers, a research monograph or a text book. The author has lectured variants of several of the chapters several times: in University of California, Berkeley, 1978, Ch. III , N, V in Ohio State Univer­ sity in Columbus, Ohio 1979, Ch. I,ll and in the Hebrew University 1979/80 Ch. I, II, III, V, and parts of VI. Moreover Azriel Levi, who has a much better name than the author in such matters, made notes from the lectures in the Hebrew University, rewrote them, and they ·are Chapters I, II and part of III , and were somewhat corrected and expanded by D. Drai, R. Grossberg and the author. Also most of XI §1-5 were lectured on and written up by Shai Ben David. Also our presentation is quite self-contained. We adopted an approach I heard from Baumgartner and may have been used by others: not proving that forcing work, rather take axiomatically that it does and go ahead to applying it. As a result we assume only knowledge of naive set theory (except some iso­ lated points later on in the book).

• Forcing (Math.)
• forcing
• proof
• set theory
• theorem

• Institute of Mathematics, The Hebrew University, Jerusalem, Israel

  Saharon Shelah

• Department of Mathematics, University of California, Berkeley, USA

  Saharon Shelah

• Department of Mathematics, Ohio State University, Columbus, USA

  Saharon Shelah

• Institute of Advanced Studies, The Hebrew University, Jerusalem, Israel

  Saharon Shelah

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