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

TL;DR

This paper constructs models under CH where Jech-Kunen trees exist without the presence of Kurepa trees, exploring the relationships between different types of omega_1-trees.

Contribution

It provides the first known models demonstrating the coexistence of Jech-Kunen trees with the absence of Kurepa trees under CH.

Findings

Existence of Jech-Kunen trees in certain models

Non-existence of Kurepa trees in these models

Models satisfy CH with 2^{omega_1} > omega_2

Abstract

By an omega_1 --tree we mean a tree of power omega_1 and height omega_1. We call an omega_1 --tree a Jech--Kunen tree if it has kappa --many branches for some kappa strictly between omega_1 and 2^{omega_1}. In this paper we construct the models of CH plus 2^{omega_1}> omega_2, in which there are Jech--Kunen trees and there are no Kurepa trees.