Essential Kurepa trees versus essential Jech–Kunen trees
نویسندگان
چکیده
منابع مشابه
Essential Kurepa Trees versus Essential Jech-Kunen Trees
By an !1{tree we mean a tree of cardinality !1 and height !1. An !1{tree is called a Kurepa tree if all its levels are countable and it has more than !1 branches. An !1{tree is called a Jech{Kunen tree if it has branches for some strictly between !1 and 2 1. 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{Kune...
متن کاملKurepa trees and Namba forcing
We show that compact cardinals and MM are sensitive to λ-closed forcings for arbitrarily large λ. This is done by adding ‘regressive’ λ-Kurepa-trees in either case. We argue that the destruction of regressive Kurepa-trees with MM requires the use of Namba forcing.
متن کاملMore on Almost Souslin Kurepa Trees
It is consistent that there exists a Souslin tree T such that after forcing with it, T becomes an almost Souslin Kurepa tree. This answers a question of Zakrzewski [6].
متن کاملCan a Small Forcing Create Kurepa Trees
In the paper we probe the possibilities of creating a Kurepa tree in a generic extension of a model of CH plus no Kurepa trees by an ω1-preserving forcing notion of size at most ω1. In the first section we show that in the Lévy model obtained by collapsing all cardinals between ω1 and a strongly inaccessible cardinal by forcing with a countable support Lévy collapsing order many ω1preserving fo...
متن کاملThe Di erences Between Kurepa Trees And Jech
By an !1{tree we mean a tree of power !1 and height !1. An !1{tree is called a Kurepa tree if all its levels are countable and it has more than !1 branches. An !1{tree is called a Jech{Kunen tree if it has branches for some strictly between !1 and 2 !1 . In x1, we construct a model of CH plus 21 > !2, in which there exists a Kurepa tree with no Jech{Kunen subtrees and there exists a Jech{Kunen ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1994
ISSN: 0168-0072
DOI: 10.1016/0168-0072(94)90021-3