Name
Abstract | ||
|---|---|---|
Generalizing Cooper’s method of quantifier elimination for Presburger arithmetic, we give a new proof that all parametric Presburger families \(\{S_t : t \in \mathbb {N}\}\) [as defined by Woods (Electron J Comb 21:P21, 2014)] are definable by formulas with polynomially bounded quantifiers in an expanded language with predicates for divisibility by f(t) for every polynomial \(f \in \mathbb {Z}[t]\). In fact, this quantifier bounding method works more generally in expansions of Presburger arithmetic by multiplication by scalars \(\{\alpha (t): \alpha \in R, t \in X\}\) where R is any ring of functions from X into \(\mathbb {Z}\). |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1007/s00153-017-0593-0 | Arch. Math. Log. |
Keywords | Field | DocType |
Presburger arithmetic, Bounded quantifiers, Elimination of imaginaries, 03C10 (Quantifier elimination, model completeness and related topics) | Quantifier elimination,Integer,Bounded quantifier,Discrete mathematics,Combinatorics,Polynomial,Divisibility rule,Presburger arithmetic,Multiplication,Mathematics,Bounding overwatch | Journal |
Volume | Issue | ISSN |
57 | 5-6 | 0933-5846 |
Citations | PageRank | References |
0 | 0.34 | 3 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| John Goodrick | 1 | 26 | 7.57 |