We study various notions of "tameness" for definably complete expansions of ordered fields. We mainly study structures with locally o-minimal open core, d-minimal structures, and dense pairs of… Expand

We consider definably complete Baire expansions of ordered fields: every definable subset of the domain of the structure has a supremum and the domain cannot be written as the union of a definable… Expand

A structure M is pregeometric if the algebraic closure is a pregeometry in all structures elementarily equivalent to M. We show that there is a corresponding abstract notion of density in models of T .Expand

We study groups and rings definable in d-minimal expansions of ordered fields. We generalize to such objects some known results from o-minimality. In particular, we prove that we can endow a… Expand

Abstract Every Henselian field of residue characteristic 0 admits a truncation-closed embedding in a field of generalised power series (possibly, with a factor set). As corollaries we obtain the… Expand

We introduce two notions of algebraic entropy for actions of cancellative right amenable semigroups $S$ on discrete abelian groups $A$ by endomorphisms; these extend the classical algebraic entropy… Expand

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.Expand