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Assuming negative of the continuum hypothesis, there is a set $ G_1 \subset \mathbb{R}$ such that if $ \aleph^\prime_1$ be cardinal of $ G_1$ , then $ \aleph_0 < \aleph^\prime_1 < \mathfrak c$ . Is there exist models of set theory in which there exist another set say $ G_2$ such that $ \aleph_0 <Read more