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Club degrees of rigidity and almost Kurepa trees

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Abstract

A highly rigid Souslin tree T is constructed such that forcing with T turns T into a Kurepa tree. Club versions of previously known degrees of rigidity are introduced, as follows: for a rigidity property P, a tree T is said to have property P on clubs if for every club set C (containing 0), the restriction of T to levels in C has property P. The relationships between these rigidity properties for Souslin trees are investigated, and some open questions are stated.

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References

  1. Abraham, U.: Construction of a rigid Aronszajn tree. In: Proceedings of the American Mathematical Society, vol. 77, no. 1, pp. 136–137 (1979)

  2. Abraham U., Shelah S.: Isomorphism types of Aronszajn trees. Israel J. Math. 50, 75–113 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  3. Devlin, K.J., Johnsbråten, H.: The Souslin Problem. Lecture Notes in Mathematics, vol. 405. Springer, Berlin (1974)

  4. Fuchs G., Hamkins J.D.: Degrees of rigidity for Souslin trees. J. Symb. Log. 74(2), 423–454 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Gaifman, H., Specker E.P.: Isomorphism types of trees. In: Proceedings of the American Mathematical Society, vol. 15, pp. 1–6 (1964)

  6. Jech T.: Automorphisms of ω 1-trees. Trans. Am. Math. Soc. 173, 57–70 (1972)

    MathSciNet  MATH  Google Scholar 

  7. Jech T.: Forcing with trees and ordinal definability. Ann. Math. Log. 7, 387–409 (1974)

    Article  MathSciNet  Google Scholar 

  8. Jech, T.: Set Theory: The Third Millenium Edition, Revised and Expanded. Springer Monographs in Mathematics. Springer, Berlin (2003)

  9. Jensen, R.B.: Automorphism properties of Souslin continua. Notices of the American Mathematical Society 16,576, 1969. Abstract #69T-E24

  10. Jin R., Shelah S.: Can a small forcing create Kurepa trees. Ann. Pure Appl. Log. 85, 47–68 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  11. Todorčević S.: Rigid Aronszajn trees. Publications de l’Institut Mathématique (Beograd), Nouvelle Série 41(27), 259–265 (1980)

    Google Scholar 

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Authors and Affiliations

  1. The College of Staten Island/CUNY, Staten Island, NY, USA

    Gunter Fuchs

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  1. Gunter Fuchs
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Correspondence to Gunter Fuchs.

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The research for this work was supported by PSC CUNY grant 60048-40-41.

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Fuchs, G. Club degrees of rigidity and almost Kurepa trees. Arch. Math. Logic 52, 47–66 (2013). https://doi.org/10.1007/s00153-012-0306-7

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  • DOI: https://doi.org/10.1007/s00153-012-0306-7

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