A variable bound by a universal quantifier can be replaced with a name for some individual in the domain.
Fourth, the quantifier rules provide no indication as to what terms or free variables must be used in their deployment.
One was a definition by quantifier elimination; see Section 2.2 below.
The existential quantifier argument will work if the ordinal stage at which the model is being constructed is a weakly compact cardinal.
The existential quantifier is an analog of the English expression " there exists ", or perhaps just " there is " .
The results of these experiments show consistent effects of all the contextual variables on quantifier judgements.
Thus in our example, the first quantifier.* grabs most of the string, while the second quantifier.* gets the empty string.
We will follow this practice of calling statements involving one of these quantifier phrases ' quantified statements '.