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Iteration of Forcing

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

Abstract

We shall now ask the following question. Suppose we start with V, extend it once by means of the forcing notion P to V[G],where G is a generic subset of P, then we take a forcing notion Q in V[G]and extend V[G]to V[G][H],where H is a subset of Q generic over V[G]; can V[G][H]be obtained from V by a single forcing extension? The answer is positive as we shall now see.

Keywords

  • Partial Order
  • Dense Subset
  • Finite Subset
  • Generic 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). Iteration of Forcing. In: Proper Forcing. Lecture Notes in Mathematics, vol 940. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21543-2_2

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  • DOI: https://doi.org/10.1007/978-3-662-21543-2_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11593-9

  • Online ISBN: 978-3-662-21543-2

  • eBook Packages: Springer Book Archive