Filter quantifier
= Filter quantifier
{title2=$\forall_{\mathcal F}x\,p(x)$}
For a proper <filter on a set>, write $\forall_{\mathcal F}x\,p(x)$ when the truth set $\{x:p(x)\}$ belongs to the filter. This quantifier preserves finite conjunctions. For an <ultrafilter> it also preserves finite disjunctions and obeys classical negation; a general proper filter need not have those latter properties.