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A model in which there are Jech-Kunen trees but there are no Kurepa trees

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Abstract

By an ω1-tree we mean a tree of power ω1 and height ω1. We call an ω1-tree a Jech-Kunen tree if it hask-many branches for somek strictly between ω1 and 2ω1. In this paper we construct the models of CH plus 2ω1 > ω2, in which there are Jech-Kunen trees and there are no Kurepa trees.

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Author information

Author notes

  1. Renling Jin

    Present address: Department of Mathematics, University of California, 94720, Berkeley, CA, USA

Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    Saharon Shelah

  2. Department of Mathematics, Rutgers University, 08903, New Brunswick, NJ, USA

    Saharon Shelah

  3. Department of Mathematics, University of Wisconsin, 53706, Madison, WI, USA

    Renling Jin

Authors
  1. Saharon Shelah
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  2. Renling Jin
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Corresponding author

Correspondence to Renling Jin.

Additional information

The research of the first author was partially supported by the Basic Research Fund, Israeli Academy of Science, Publ. No. 466.

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Shelah, S., Jin, R. A model in which there are Jech-Kunen trees but there are no Kurepa trees. Israel J. Math. 84, 1–16 (1993). https://doi.org/10.1007/BF02761687

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  • DOI: https://doi.org/10.1007/BF02761687

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