Preservation of AD via forcings

Daisuke Ikegami, Nam Trang

We show that assuming $\mathsf{ZF}+{\mathsf{AD}}^{+}+$ "$V=\mathrm{L}(\wp (\mathbb{R}))$", any poset which increases $\Theta$ does not preserve the truth of $\mathsf{AD}$. We…