I'm trying to understand rules of relational model as originally defined by Edgar Codd in 1970.
Specifically I'm interested whether referential integrity is part of his relational model or not. I'll try to demonstrate on following example (just to make this question pretty):
Customers
+------+------------
| Name | Address
|------+------------
| John | ....
| Mike | ....
| Kate | ....
+------+------------
Invoices
+------+------------
| ID | Customer
|------+------------
| 1 | John
| 2 | John
| 3 | Mary
+------+------------
Now, obviously as you can see, we have one invoice where customer (foreign key) is Mary. Would this violate his relational model? Would Edgar Codd look at this and say, gee, what the heck? Or would he say, it's perfectly fine...
This is theoretical question.
For a language to be considered relationally complete (a phrase coined by Codd) it must support a set of relational operators, known as a relational algebra. Note there is no one true relational algebra: Codd proposed the first one but others have since refined and built upon Codd's (e.g. The Third Manifesto) and I'm sure he would see this as right and proper.
Referential integrity is not a relational operator and therefore is not a requirement for relational completeness of a language. Whether referential integrity constraints are a useful or necessary feature of a DBMS is another matter.