Results on the Generic Kurepa Hypothesis

Archive for Mathematical Logic 30 (1):13-27 (1990)
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Abstract

K.J. Devlin has extended Jensen's construction of a model ofZFC andCH without Souslin trees to a model without Kurepa trees either. We modify the construction again to obtain a model with these properties, but in addition, without Kurepa trees inccc-generic extensions. We use a partially defined ◊-sequence, given by a fine structure lemma. We also show that the usual collapse ofκ Mahlo toω 2 will give a model without Kurepa trees not only in the model itself, but also inccc-extensions

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Citations of this work

On the existence of strong chains in ℘(ω1)/fin.Piotr Koszmider - 1998 - Journal of Symbolic Logic 63 (3):1055 - 1062.
On constructions with 2-cardinals.Piotr Koszmider - 2017 - Archive for Mathematical Logic 56 (7-8):849-876.
Easton's theorem for the tree property below ℵ.Šárka Stejskalová - 2021 - Annals of Pure and Applied Logic 172 (7):102974.

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References found in this work

Set theory.Thomas Jech - 1981 - Journal of Symbolic Logic.
Constructibility.Keith J. Devlin - 1987 - Journal of Symbolic Logic 52 (3):864-867.
Coding the Universe.A. Beller, R. Jensen & P. Welch - 1982 - Cambridge University Press.
Multiple Forcing.T. Jech - 1989 - Journal of Symbolic Logic 54 (3):1112-1113.

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