Where Do Structures Come From?

Abstract

The compactness theorem, Theorem 11.2, is one of the most frequently used basic tools of model theory. It implies that for every structure with an infinite domain there is another structure that is very similar but not isomorphic to the given one. We will see a toy example that shows how such structure could be used to study number-theoretic problems. A more advanced application is given in Appendix A.5.