Consequences of W_{ℵ1}: PS1 and P-space existence for 2^Y[[Y]^{≤ω}]

Determine whether the comparability principle W_{ℵ1} implies either of the following in ZF: (a) for every uncountable set X there exists an uncountable Y⊆X such that 2^{Y}[[Y]^{≤ω}] is a P-space; or (b) PS1 (that for every uncountable set X there exists an uncountable Y⊆X such that S(Y,[Y]^{≤ω}) is a P-space).

Background

After analyzing consequences of W_{ℵ1} in permutation models and its relations to CUC and other principles, the authors point out that it is not known in ZF whether W_{ℵ1} suffices for the P-space existence properties encapsulated by PS1 or for the analogous statement about the product topology 2^{Y}[[Y]^{≤ω}].