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Does W_{ℵ1} imply CUC in ZF?

Determine whether the comparability principle W_{ℵ1} implies the Countable Union Theorem (CUC) in ZF.

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Background

The authors show that W_{ℵ1} together with cf(ℵ1)=ℵ1 implies CUC and that in permutation models W_{ℵ1} implies CUC (since cf(ℵ1)=ℵ1 holds there). However, they explicitly note that in ZF alone it is unknown whether W_{ℵ1} implies CUC.

References

Moreover, it is also unknown if $\mathbf{W}{\aleph{1}}$ implies $\mathbf{CUC}$ in $\mathbf{ZF}$.

— Constructing crowded Hausdorff $P$-spaces in set theory without the axiom of choice (2510.11935 - Tachtsis et al., 13 Oct 2025) in Section 9, Remark rem:W_aleph