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Morass-like constructions of ℵ2-trees in L

Part of the Lecture Notes in Mathematics book series (LNM,volume 872)

Abstract

Using a simplified version of the fine structure theory required for the construction of a morass, we show how to construct Souslin and Kurepa ℵ2-trees as limits of directed systems of countable trees. These techniques were originally developed by us in order to obtain a Souslin ℵ2-tree T such that the reduced power tree Tω/D, where D is non-principal, uniform filter on ω, is a Kurepa ℵ2-tree. However, subsequent to our work, R. Laver obtained a much simpler proof, so we do not include this result here. Rather the present account is largely expository in nature.

Keywords

  • Limit Point
  • Large Cardinal
  • Distinct Branch
  • Aronszajn Tree
  • Countable Tree

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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References

  1. K.J. Devlin, Aspects of Constructibility. Springer Lecture Notes 354 (1973).

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  2. —, Constructibility. Springer, to appear.

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  6. J.H. Silver, The Independence of Kurepa’s Conjecture and Two-Cardinal Conjectures in Model Theory. AMS Proc. Symp. in Pure Maths. XIII, Part I, 383–390.

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© 1981 Springer-Verlag

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Devlin, K.J. (1981). Morass-like constructions of ℵ2-trees in L. In: Jensen, R.B., Prestel, A. (eds) Set Theory and Model Theory. Lecture Notes in Mathematics, vol 872. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098617

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  • DOI: https://doi.org/10.1007/BFb0098617

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10849-8

  • Online ISBN: 978-3-540-38757-2

  • eBook Packages: Springer Book Archive