TITLE: Symbols for Quantifiers Other Than $\forall$ and $\exists$
QUESTION [8 upvotes]: The symbols $\forall$ and $\exists$ denote "for all" and "there exists" quantifiers. In some papers, I saw the (not so common) quantifiers $Я$ and $\exists^+$, denoting "for a randomly chosen element of" and "for most elements in", respectively.
Are there other symbols for quantifiers?
I'm specially interested in quantifiers for:

for all but finitely many elements of...
for infinitely many elements of...


Edit: After seeing some of the comments, I found the list of logic symbols and the table of mathematical symbols, which I could be useful for others.

REPLY [2 votes]: Somehow it is missing that $∃_∞$ and $∀_∞$ both are first order definable when for example the domain is the natural numbers. We then have:
there are infinitely many
$∃_∞x A(x) \Leftrightarrow ∀y ∃x (x \geq y \wedge A(x))$
for all but finitely many
$∀_∞x A(x) \Leftrightarrow ∃y ∀x (x \geq y \Rightarrow A(x))$
Not all exotic quantifiers are that simple, see for example:
Modal Quantifiers, Natasha Alechina - 1995
http://www.cs.nott.ac.uk/~psznza/papers/Alechina:95d.pdf