5 citations · 18 across the 16 of their papers we have counts for
20 papers
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…
Periodic behavior in families of numerical and affine semigroups via parametric Presburger arithmetic
Tristram Bogart, John Goodrick, Kevin Woods
Let be polynomial functions of . For fixed , let be the numerical semigroup generated by $f_1(n),\ldots,f_k(n)…
A parametric version of LLL and some consequences: parametric shortest and closest vector problems
Tristram Bogart, John Goodrick, Kevin Woods
Given a parametric lattice with a basis given by polynomials in Z[t], we give an algorithm to construct an LLL-reduced basis whose elements are eventually quasi-polynomial in t: th…
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…