Archive for Mathematical Logic 32 (5):369-379 (1993)

Abstract
By an ω1 we mean a tree of power 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 $2^{\omega _1 }$ . In Sect. 1, we construct a model ofCH plus $2^{\omega _1 } > \omega _2$ , in which there exists a Kurepa tree with not Jech-Kunen subtrees and there exists a Jech-Kunen tree with no Kurepa subtrees. This improves two results in [Ji1] by not only eliminating the large cardinal assumption for [Ji1, Theorem 2] but also handling two consistency proofs of [Ji1, Theorem 2 and Theorem 3] simultaneously. In Sect. 2, we first prove a lemma saying that anAxiom A focing of size ω1 over Silver's model will not produce a Kurepa tree in the extension, and then we apply this lemma to prove that, in the model constructed for Theorem 2 in [Ji1], there exists a Jech-Kunen tree and there are no Kurepa trees
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DOI 10.1007/BF01409969
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References found in this work BETA

Set Theory.Thomas Jech - 1981 - Journal of Symbolic Logic.
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.
Some Independence Results Related to the Kurepa Tree.Renling Jin - 1991 - Notre Dame Journal of Formal Logic 32 (3):448-457.

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Citations of this work BETA

Can a Small Forcing Create Kurepa Trees.Renling Jin & Saharon Shelah - 1997 - Annals of Pure and Applied Logic 85 (1):47-68.
Essential Kurepa Trees Versus Essential Jech–Kunen Trees.Renling Jin & Saharon Shelah - 1994 - Annals of Pure and Applied Logic 69 (1):107-131.

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