Bounding quantification in parametric expansions of Presburger arithmetic

@article{Goodrick2018BoundingQI,
  title={Bounding quantification in parametric expansions of Presburger arithmetic},
  author={John Goodrick},
  journal={Arch. Math. Log.},
  year={2018},
  volume={57},
  pages={577-591}
}
Generalizing Cooper’s method of quantifier elimination for Presburger arithmetic, we give a new proof that all parametric Presburger families {St : t ∈ N} (as defined by Woods in [8]) are definable by formulas with polynomially bounded quantifiers in an expanded language with predicates for divisibility by f(t) for every polynomial f ∈ Z[t]. In fact, this quantifier bounding method works more generally in expansions of Presburger arithmetic by multiplication by scalars {α(t) : α ∈ Z, t ∈ X… CONTINUE READING