Models of true arithmetic are integer parts of nice real closed fields

TL;DR

The paper establishes that every model of true arithmetic can be embedded as an integer part within an exponential real closed field that shares the same elementary properties as the real numbers with exponentiation.

Contribution

It demonstrates a novel connection between models of true arithmetic and exponential real closed fields, extending the understanding of their structural relationships.

Findings

Each model of true arithmetic is an integer part of an exponential real closed field.

Such fields are elementary equivalent to the real numbers with exponentiation.

The work deepens the link between arithmetic models and real closed fields with exponentiation.

Abstract

Exploring further the connection between exponentiation on real closed fields and the existence of an integer part modelling strong fragments of arithmetic, we demonstrate that each model of true arithmetic is an integer part of an exponential real closed field that is elementary equivalent to the reals with exponentiation.