Order types of models of reducts of Peano Arithmetic and their fragments
Lorenzo Galeotti, Benedikt Löwe
Abstract:
It is well-known that non-standard models of Peano Arithmetic have order type N + Z·D where D is a dense linear order without first or last element. Not every order of the form N + Z·D is the order type of a model of Peano Arithmetic, though; in general, it is not known how to characterise those D for which this is the case. In this paper, we consider syntactic fragments of Peano Arithmetic (both with and without induction) and study the order types of their non-standard models.