  Having defined the syntax of  L(κ,λ),  we next sketch its semantics. Since the extralogical symbols of  L(κ,λ)  are just those  of  L, and it is these symbols which determine the form of the structures in which a given first-order language is to be interpreted, it is natural to define an  L(κ,λ)-structure  to be simply an  L-structure.  The notion of a formula of  L(κ,λ)  being satisfied in an  L-structure A (by a sequence of elements from the domain of A) is defined in the same inductive manner as for formulas of  L  except that we must add two extra clauses corresponding to the clauses for  ∧Φ  and ∃Xφ in the definition of preformula. In these two cases we naturally define: