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Proper Forcing

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

Abstract

When we iterate we are faced with the problem of obtaining for the iteration the good properties of the single steps of iteation. Usually the worst possible vice of a forcing notion is that it collapses 1. The virtue of not collapsing 1 is not inherited by the iteration from its single components. As we saw, the virtue of the c.c.c. is inherited by the FS iteration from its components. However the c.c.c. is too strong a requirement. We shall look for a weaker requirement which is more naturally connected to the property of not collapsing l, and which is inherited by iterations.

Keywords

  • Dense Subset
  • Order Type
  • Generic Subset
  • Partial Algebra
  • Force Notion

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). Proper Forcing. In: Proper Forcing. Lecture Notes in Mathematics, vol 940. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21543-2_3

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  • DOI: https://doi.org/10.1007/978-3-662-21543-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11593-9

  • Online ISBN: 978-3-662-21543-2

  • eBook Packages: Springer Book Archive