Representing Scott sets in algebraic settings

TL;DR

This paper demonstrates that for any Scott set, there exist algebraic structures such as S-saturated real closed fields and models of Presburger arithmetic, bridging set theory and algebra.

Contribution

It establishes the existence of algebraic models corresponding to any given Scott set, extending the understanding of their algebraic representations.

Findings

Existence of S-saturated real closed fields for any Scott set

Existence of models of Presburger arithmetic for any Scott set

Bridging set-theoretic and algebraic structures

Abstract

We prove that for every Scott set $S$ there are $S$-saturated real closed fields and models of Presburger arithmetic.