We study first-order expansions of ordered fields that are definably complete, and moreover
either are locally o-minimal, or have a locally o-minimal open core. We give a …

A first-order expansion of the R-vector space structure on R does not define every compact
subset of every R n if and only if topological and Hausdorff dimension coincide on all closed …

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 …

Metric dimensions and tameness in expansions of the real field Page 1 TRANSACTIONS OF
THE AMERICAN MATHEMATICAL SOCIETY Volume 373, Number 2, February 2020, Pages …

Observation: Type C⇒ No model-theoretic tameness. Observation: O-minimality⇒ Type A.
Observation: NTP2⇒ Type A. Observation: Type B interprets (N, P (N),+ 1,∈), can be …

Let R be an expansion of the ordered real additive group. When R is o-minimal, it is known
that either R defines an ordered field isomorphic to (R,<,+,·) on some open subinterval I⊆ R …

We prove the following theorem: let R˜ be an expansion of the real field R‾, such that every
definable set (I) is a uniform countable union of semialgebraic sets, and (II) contains a …

In contrast to the importance of real numbers for mathematical sciences a metamathematical
approach to real numbers has never been developed systematically, a gap this book …