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What does a dot (.) mean in predicates?
$\forall a \in A. \exists d \in D. H(a,d)$
Especially, how is the above different to
$ \exists d \in D. \forall a \in A. H(a,d)$
I've never seen this used in German lecture scripts.
The dot just means "such that"; it's often omitted.
The difference between the two formulas is the difference between "everybody has a mother" and "there is somebody who is everybody's mother."
Well, in $\forall x. P(x)$, the "such that" reading of the dot (or the space, if we don't like to write dots) doesn't make sense grammatically as it does for the existential. One could say, I suppose, "it holds that", or something like that.
Required, but never shown