From the theorem it follows for instance that if some first-order sentence holds for every field of characteristic zero, then there exists a constant *p* such that the sentence holds for every field of characteristic larger than *p*. This can be seen as follows: suppose *S* is the sentence under consideration. Then its negation ~*S*, together with the field axioms and the infinite series of sentences 1+1 ≠ 0, 1+1+1 ≠ 0, ... is not satisfiable by assumption. Therefore a finite subset of these sentences is not satisfiable, meaning that *S* holds in those fields which have large enough characteristic.

Also, it follows from the theorem that any theory that has an infinite model has models of arbitrary large cardinality. So, for instance, there are nonstandard models of Peano arithmetic with uncountably many natural numbers. The nonstandard analysis is another example where infinite natural numbers appear, a possibility that cannot be excluded by any axiomatization - also a consequence of the compactness theorem.