Boolean failure of the cofinite-filter quantifier
= Boolean failure of the cofinite-filter quantifier
{c}
The even and odd integers are both absent from the <cofinite filter>, but their union is present. Thus its <filter quantifier> need not turn a disjunction into the disjunction of quantified assertions, and failure of a quantified assertion need not imply truth of its quantified negation. An <ultrafilter> restores both laws by deciding each set against its complement.