 One interesting implication of the existence of inconsistent models of arithmetic is that some of them are finite (unlike the classical non-standard models). This means that there are some significant applications in the metamathematical theorems. For example, the classical Löwenheim-Skolem theorem states that \(Q\) (Robinson’s arithmetic which is a fragment of Peano arithmetic) has models of every infinite cardinality but has no finite models. But, \(Q\) can be shown to have models of finite size too by referring to the inconsistent models of arithmetic.