Interpreting the weak monadic second order theory of the ordered rationals

TL;DR

This paper demonstrates that the weak monadic second order theory of the ordered rationals can be interpreted within its automorphism group, linking logical theories with group automorphisms.

Contribution

It establishes a first order interpretability of the weak monadic second order theory in the automorphism group of the ordered rationals, revealing a deep connection between logic and symmetry.

Findings

Weak monadic second order theory is interpretable in automorphism group

Links logical theories with automorphism groups of structures

Provides new insights into the structure of ordered rationals

Abstract

We show that the weak monadic second order theory of the structure $({\mathbb Q}, <)$ is first order interpretable in its automorphism group.