# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Planting Kurepa trees and killing Jech-Кunen trees in a model by using one inaccessible cardinal

### Tom 141 / 1992

Fundamenta Mathematicae 141 (1992), 287-296 DOI: 10.4064/fm-141-3-287-296

#### Streszczenie

By an $ω_1$- tree we mean a tree of power $ω_1$ and height $ω_1$. Under CH and $2^{ω_{1}} > ω_2$ we call an $ω_1$-tree a Jech-Kunen tree if it has κ-many branches for some κ strictly between $ω_1$ and $2^{ω_{1}}$. In this paper we prove that, assuming the existence of one inaccessible cardinal, (1) it is consistent with CH plus $2^{ω_{1}} > ω_2$ that there exist Kurepa trees and there are no Jech-Kunen trees, which answers a question of [Ji2], (2) it is consistent with CH plus $2^{ω_{1}} = ω_4$ that there only exist Kurepa trees with $ω_{3}$-many branches, which answers another question of [Ji2].

#### Autorzy

• Saharon Shelah
• R. Jin

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