Assume $ \mathsf{ZF} + \mathsf{DC}$ . Must there exist an injection from $ \aleph_2$ to $ \mathcal{P}(\mathbb{R})$ ? If not, what is the consistency strength of the nonexistence of such an injection? I hope I’m not missing something obvious. Here are my thoughts so far: There is always a surjection from $ \mathcal{P}(\mathbb{R})$ to $Read more
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