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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References
Beller, A., Jensen, R.B., Welch, P.: Coding the universe. Cambridge London: Cambridge University Press 1982
Devlin, K.J.: ℵ1-trees. Ann. Math. Logic13, 267–330 (1978)
Devlin, K.J.: Concerning the consistency of the Souslin hypothesis with the continuum hypothesis. Ann. Math. Logic19, 115–125 (1980)
Devlin, K.J.: Constructibility. Berlin Heidelberg New York: Springer 1984
Devlin, K.J., Johnsbraten, H.: The Souslin problem. (Lect. Notes Math., vol. 405) Berlin Heidelberg New York: Springer 1974
Jensen, R.B.: ◊ impliesGKH, (handwritten notes)
Jech, T.: Set theory. New York: Academic Press 1978
Jech, T.: Multiple forcing. Cambridge: Cambridge University Press 1986
Kunen, K.: Set theory. Amsterdam: North-Holland 1980
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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