sentences:  Each quantifier formula_6 is relativized to a structure, since each quantifier is viewed as a family of relations (between relations) on that structure.For a concrete example, take the universal and existential quantifiers ∀ and ∃, respectively.Their truth conditions can be specified as
  
  where formula_9 is the singleton whose sole member is dom("A"), and formula_10 is the set of all non-empty subsets of dom("A") (i.e.