Annals of Pure and Applied Logic 69 (1):107-131 (1994)

Abstract
By an ω1-tree we mean a tree of cardinality ω1 and height ω1. An ω1-tree is called a Kurepa tree if all its levels are countable and it has more than ω1 branches. An ω1-tree is called a Jech–Kunen tree if it has κ branches for some κ strictly between ω1 and 2ω1. A Kurepa tree is called an essential Kurepa tree if it contains no Jech–Kunen subtrees. A Jech–Kunen tree is called an essential Jech–Kunen tree if it is no Kurepa subtrees. In this paper we prove that it is consistent with CH and 2ω1 #62; ω2 that there exist essential Kurepa trees and there are no essential Jech–Kunen trees, it is consistent with CH and 2ω1 #62; ω2 plus the existence of a Kurepa tree with 2ω1 branches that there exist essential Jech–Kunen trees and there are no essential Kurepa trees. In the second result we require the existence of a Kurepa tree with 2ω1 branches in order to avoid triviality
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DOI 10.1016/0168-0072(94)90021-3
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References found in this work BETA

[Omnibus Review].Kenneth Kunen - 1969 - Journal of Symbolic Logic 34 (3):515-516.
Trees.Thomas J. Jech - 1971 - Journal of Symbolic Logic 36 (1):1-14.
A Model in Which Every Kurepa Tree is Thick.Renling Jin - 1991 - Notre Dame Journal of Formal Logic 33 (1):120-125.
The Differences Between Kurepa Trees and Jech-Kunen Trees.Renling Jin - 1993 - Archive for Mathematical Logic 32 (5):369-379.

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