Finite Models of Eleimentaxy Recursive Nonstandard Analysis

This paper provides a new proof of the consistency of the formal system presented by Chuaqui and Suppes in [2, 9). First, a simpler, yet stronger, system, called Elementary Recursive Nonstandard Analysis, ERNA, will be provided. Indeed, it will be shown that ERNA proves all of the theorems of the Chuaqui and Suppes system. Then a finitary consistency proof of ERNA dl be given; in particular, we will show that PXA, the system of primitive recursive arithmetic, which is generally recognized as capturing Hilbert’s notion of finitaryl proves the consistency of ERNA. Rom the consistency proof we can extract a constructive method for obtaining finite approximations of models of nonstandard analysis. We present an isomorphism theorem for models that are finite substructures of infinite models.