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Results on the Generic Kurepa Hypothesis

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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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Jensen, R.B., Schlechta, K. Results on the Generic Kurepa Hypothesis. Arch Math Logic 30, 13–27 (1990). https://doi.org/10.1007/BF01793783

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  • DOI: https://doi.org/10.1007/BF01793783

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