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More forcing notions imply diamond

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Abstract.

We prove that the Sacks forcing collapses the continuum onto \({\frak d}\), answering the question of Carlson and Laver. Next we prove that if a proper forcing of the size at most continuum collapses \(\omega_2\) then it forces \(\diamondsuit_{\omega_{1}}\).

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel, , , , , , IL

    Andrzej Rosłanowski

  2. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel, , , , , , IL

    Saharon Shelah

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  1. Andrzej Rosłanowski
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  2. Saharon Shelah
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Received July 4, 1994

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Rosłanowski, A., Shelah, S. More forcing notions imply diamond . Arch Math Logic 35, 299–313 (1996). https://doi.org/10.1007/s001530050047

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  • DOI: https://doi.org/10.1007/s001530050047

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