 Baire property in the ordinary infinite-subset topology

A family $Y\subseteq [\mathbb{N}{]}^{\omega }$ is $\tau$-Baire when $Y△O$ is meagre for some ordinarily open family $O$. This is weaker than the corresponding regularity in the star topology. A meagre set meeting every Ramsey cone in both colours has the ordinary Baire property while failing to be a Ramsey set of infinite subsets.