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α- Properness and Not Adding Reals

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

Abstract

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.

Keywords

  • Pairwise Disjoint
  • Dense Subset
  • Order Type
  • Open Dense Subset
  • Uniformization Property

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1982 Springer-Verlag Berlin Heidelberg

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Shelah, S. (1982). α- Properness and Not Adding Reals. In: Proper Forcing. Lecture Notes in Mathematics, vol 940. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21543-2_5

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  • DOI: https://doi.org/10.1007/978-3-662-21543-2_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11593-9

  • Online ISBN: 978-3-662-21543-2

  • eBook Packages: Springer Book Archive