Ordered Structures

We know how to prove basic results about FO; so now we start adding things to FO. One way to make FO more expressive is to include additional operations on the universe. For example, in database applications, data items stored in a database are numbers, strings, etc. Both numbers and strings could be ordered; on numbers we have arithmetic operations, on strings we have concatenation, substring tests, and so on. As query languages routinely use those operations, one may want to study them in the context of FO.