Wikipedia defines quantifiers as an "operator".
The word "operator" means "operation" (a function) or "logical operator" (logical connective).
I also read that an atomic formula cannot have quantifiers.
Because atomic formulas are defined with the condition of having no logical connectives, I wonder if quantifiers not being allowed is because of this.
Is a quantifier a logical connective?
Connectives and quantifiers are two different types of operators.
An n-ary connective is an operator which takes n formulas and gives a new formula.
A quantifier is an operator which takes a formula and a variable and gives a new formula.
Atomic formulas have no operators, so no connectives and no quantifiers.