Village wives and the public infidelity announcement

In a village, each wife knows whether every other husband is unfaithful but not whether her own is, and a wife who deduces that her husband cheats evicts him the next morning. All wives are perfect logicians and hear everything announced publicly. A visitor publicly states that at least one husband is unfaithful. Nothing happens until the morning of day $10$, when the first evictions take place. How many husbands are thrown out?

10. By induction, if there are $k$ cheaters, each of their wives sees $k-1$ and waits to see whether those are evicted by day $k-1$; when nothing happens she concludes her own husband cheats. So all $k$ evictions happen together on day $k$, giving $k=10$.