variables and function symbols alone do not suffice for formulating in a first-order language statements about a structure
. for this,
must have symbols that can be used to denote the basic relations of
. a symbol designed to denote an
-ary relation is called an
-ary predicate symbol.
a predicate represents a property or relation. it can be seen as a total function whose range is
where 1 denotes membership of the relation and 0 otherwise.