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
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References
K.J. Devlin, Aspects of Constructibility. Springer Lecture Notes 354 (1973).
—, Constructibility. Springer, to appear.
T.J. Jech. Trees. Journal of Symbolic Logic 36, (1971), 1–14.
R. Laver & S. Shelah. The ℵ 2 -Souslin Hypothesis.
W.J. Mitchell, Aronszajn Trees and the Independence of the Transfer Property. Annals of Math. Logic 5, (1972), 21–46.
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
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