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@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} }

- Published 2018 in Arch. Math. Log.
DOI:10.1007/s00153-017-0593-0

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