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. the power set of dom("A") minus the empty set). In other words, each quantifier is a family of properties on dom("A"), so each is called a "monadic" quantifier. Any quantifier defined as an "n" > 0-ary relation between properties on dom("A") is called "monadic". Lindström introduced polyadic ones that are "n" > 0-ary relations between relations on domains of structures.