I have seen proofs that under CH, Namba forcing does not add reals, and thus preserves $\omega_1$. How do you prove in ZFC alone that it preserves $\omega_1$? I have also seen the stronger claim that it preserves stationary subsets of $\omega_1$, so please provide a reference for that also if possible.
2026-03-28 01:46:23.1774662383
Why does Namba forcing preserve $\omega_1$?
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