Let 
be a language of the first-order
logic. Assume that the language 
has the following sets of nonlogical symbols:
1. 
is the set of constant symbols of 
. (These are nullary function symbols.)
2. 
is the set of predicate symbols of 
, and for each 
, 
is the arity of 
.
The symbols in 
are also called relation symbols of the language 
.
3. 
is the set of function symbols of 
, and for each 
, 
is the arity of 
. The symbols in 
are also called operation symbols of the language 
.
4. 
is the universal
quantifier symbol of 
.
A structure for 
is a tuple 
,
, 
where 
is a set (called the underlying set of 
), and the following hold:
1. For each 
,
,
2. For each 
,
,
3. For each 
,
.
