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More forcing notions imply diamond

Andrzej Rosłanowski·Saharon Shelah
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Abstract

We prove that the Sacks forcing collapses the continuum onto the dominating number 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 diamond_{omega_1} .

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Andrzej Rosłanowski, Saharon Shelah. 1994-08-15. More forcing notions imply diamond. https://arxiv.org/abs/math/9408215

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