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

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

Abstract

Here we present how to iterate forcing satisfying the \(\bar M\)-c.c. for an oracle \(\bar M\). This enables us, in some sense, to “construct” the set of reals in ω 2 steps with omitting types along the way (i.e., imitating constructions of model theory). We use it to prove the consistency of “P(ω) /finite has no non-trivial automorphism”, which is equivalent to “β(N) −N has only trivial homeomorphisms”.

Keywords

  • Main Lemma
  • Force Notion
  • Finite Support
  • Infinite Subset
  • Maximal Antichain

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). On oracle-c.c. and “P(ω)/ finite has no non-trivial automorphism”. In: Proper Forcing. Lecture Notes in Mathematics, vol 940. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21543-2_4

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  • DOI: https://doi.org/10.1007/978-3-662-21543-2_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11593-9

  • Online ISBN: 978-3-662-21543-2

  • eBook Packages: Springer Book Archive