We prove that in the Miller model, every M-separable space of the form C_p(X), where X is metrizable and separable, is productively M-separable, i.e., C_p(X)xY is M-separable for every countable M-separable Y. Remark: The journal Annals of Pure and Applied Logic is ranked in the top quarter of the SCI list for all mathematics journals.
We prove that the Hurewicz property is not preserved by finite products in the Miller model. This is a consequence of the fact that Miller forcing preserves ground model gamma-spaces. Remark: The journal Proceedings of the American Mathematical Society is ranked in the second quarter of the SCI list for all mathematics journals.
We prove that in the Laver model for the consistency of the Borel's conjecture, the product of any two H-separable spaces is M-separable.