It isn’t for all repeated vowels; only for when the 2 vowels don’t make a single sound. So “chicken coop” wouldn’t have a dieresis
It would if the chickens formed a business structure that was owned and democratically controlled by its member-owners.
Unless it was a chicken coöp... One of few cases it actually resolves an ambiguity!
It would if the chickens formed a business structure that was owned and democratically controlled by its member-owners.