5 citations · 18 across the 16 of their papers we have counts for
17 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…
Parametric Presburger Arithmetic: Complexity of Counting and Quantifier Elimination
Tristram Bogart, John Goodrick, Danny Nguyen +1
We consider an expansion of Presburger arithmetic which allows multiplication by parameters . A formula in this language defines a parametric set $S_\mathbf{t}…
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…
Left-ordered inp-minimal groups
Jan Dobrowolski, John Goodrick
We prove that any left-ordered inp-minimal group is abelian, and we provide an example of a non-abelian left-ordered group of dp-rank 2.
Bounding quantification in parametric expansions of Presburger arithmetic
John Goodrick
We generalize Cooper's method of quantifier elimination for classical Presburger arithmetic to give a new proof that all parametric Presburger families (as defined by Kevin Woods)…