Interpreting the monadic second order theory of one successor in expansions of the real line

Abstract

We give sufficient conditions for a first order expansion of the real line to define the standard model of the monadic second order theory of one successor. Such an expansion does not satisfy any of the combinatorial tameness properties defined by Shelah, such as $\text{NIP}$ or even ${\text{NTP}}_2$. We use this to deduce the first general results about definable sets in ${\text{NTP}}_2$ expansions of $(\mathbb{R},<,+)$.

References in corpus (1)

• Expansions of the reals which do not define the natural numbers