Products of HH-separable spaces in the Laver model

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

Non-commutative separability and group actions

We give conditions for the skew group ring S * G to be strongly separable and H-separable over the ring S. In particular we show that the H-separability is equivalent to S being central Galois extension. We also look into the H-separability of the ring S over the fixed subring R under afaithful action of a group G. We show that such a chain: S * G H-separable over S and S H-separable over R cannot occur, and that the centralizer of R in S is an Azumaya algebra in the presence of a central element of trace one