18 citations · 26 across the 9 of their papers we have counts for
11 papers · 1 filter
Discrete sets definable in strong expansions of ordered Abelian groups
Alfred Dolich, John Goodrick
We study the structure of infinite discrete sets D definable in expansions of ordered Abelian groups whose theories are strong and definably complete, with particular emphasis on t…
Topological properties of definable sets in ordered Abelian groups of burden 2
Alfred Dolich, John Goodrick
We obtain some new results on the topology of unary definable sets in densely ordered Abelian groups of burden groups of burden 2. In the special case in which the structure has dp…
Connectedness in structures on the real numbers: o-minimality and undecidability
Alfred Dolich, Chris Miller, Alex Savatovsky +1
We initiate an investigation of structures on the set of real numbers having the property that path components of definable sets are definable. All o\nobreakdash-\hspace{0pt}minima…
A characterization of strongly dependent ordered Abelian groups
Alfred Dolich, John Goodrick
We characterize all ordered Abelian groups whose first order theory in the language {+,<} is strongly dependent. The main result of this note was obtained independently by Halevi-H…
Strong theories of ordered abelian groups
Alfred Dolich, John Goodrick
We consider strong expansions of the theory of ordered abelian groups. We show that the assumption of strength has a multitude of desirable consequences for the structure of defina…
Tame topology over definable uniform structures
Alfred Dolich, John Goodrick
A visceral structure on M is given by a definable base for a uniform topology on its universe in which all basic open sets are infinite and any infinite definable subset X of M has…