Proper Forcing pp 153-194 | Cite as

α- Properness and Not Adding Reals

  • Saharon Shelah
Part of the Lecture Notes in Mathematics book series (LNM, volume 940)


Next to not collapsing 1 not adding reals seems the most natural requirement on forcing notion. There are many works deducing various assertions from CH and many others who did it from diamond of 1. If we want to show that the use of diamond is necessary, we usually have to build a model of ZFC in which CH holds but the assertion fails, by iterating suitable forcing. A crucial part in such a proof is showing that the forcing notions do not add reals even when we iterate them.


Pairwise Disjoint Dense Subset Order Type Open Dense Subset Uniformization Property 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • Saharon Shelah
    • 1
    • 2
    • 3
    • 4
  1. 1.Institute of MathematicsThe Hebrew UniversityJerusalemIsrael
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  3. 3.Department of MathematicsOhio State UniversityColumbusUSA
  4. 4.Institute of Advanced StudiesThe Hebrew UniversityJerusalemIsrael

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